- Analysis-seminar - Mailing list — Dipartimento di Matematica, UniPI

seminario Roberto Ognibene
by Alessandra Pluda 05 Apr '23

05 Apr '23

Cari tutti, diversamente da quanto apparso sul notiziario del dipartimento, il seminario di Roberto Ognibene si terrà domani Mercoledì 5 Aprile, dalle 18:00 alle 19:00, in AULA MAGNA del Dipartimento di Matematica. A presto, Alessandra

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seminario Riccardo Montalto
by Alessandra Pluda 03 Apr '23

03 Apr '23

Cari tutti, anche se è già apparso sul notiziario del dipartimento, segnalo il seminario di domani di Riccardo Montalto. A presto, Alessandra martedì 4 aprile, ore 13:30-14:30, aula seminari Seminario del ciclo di Analisi Stocastica TITOLO: Construction on quasi-periodic nonlinear waves in fluid mechanics Abstract: In this talk I will discuss some recent results on Euler and Navier Stokes equations concerning the construction of quasi-periodic solutions and the problem of the inviscid limit for the Navier Stokes equation. I will discuss the following results: 1) Construction of quasi-periodic solutions for the Euler equation with a time quasi-periodic external force, bifurcating from a constant, diophantine velocity field 2) I shall discuss the inviscid limit problem from the perspective of KAM theory, namely I shall prove the existence of quasi-periodic solutions of the Navier Stokes equation converging to the one of the Euler equation constructed in 1) . The main difficulty is that this is a singular limit problem. We overcome this difficulty by implementing a normal form methods which allow to prove sharp estimates (global in time) w.r. to the viscosity parameter 3) (time permittiing) I also discuss the construction of quasi-periodic traveling waves bifurcating from the Couette flow for the autonomous 2D Euler equation. These works are based on collaborations with Luca Franzoi and Nader Masmoudi

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seminario di Francesca Prinari, giovedì ore 17
by Alessandra Pluda 28 Mar '23

28 Mar '23

Cari tutti, questa settimana ci sarà un seminario di analisi di Francesca Prinari (UNIPI): Giovedì 30 Marzo Aula Riunioni, ore 17:00 Seguono titolo e abstract. Un caro saluto, Alessandra, Jacopo e Maria Stella. Titolo: Sobolev embedding and distance functions Abstract: On a general open set of the euclidean space, we study the relation between the embedding of the homogeneous Sobolev space $D^{1,p}_0$ into $L^q$ and the summability properties of the distance function. We prove that in the superconformal case (i.e. when $p$ is larger than the dimension) these two facts are equivalent, while in the subconformal and conformal cases (i.e. when p is less than or equal to the dimension) we construct counterexamples to this equivalence. In turn, our analysis permits to study the asymptotic behaviour of the positive solution of the Lane-Emden equation for the p-Laplacian with sub-homogeneous right-hand side, as the exponent p diverges to $+\infty$. (a joint work with L. Brasco and A.C. Zagati).

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Giornata di seminari dei dottorandi e perfezionandi in analisi
by Alessandra Pluda 22 Mar '23

22 Mar '23

Cari tutti, settimana prossima ci sarà una giornata dedicata a seminari di nostri dottorandi e perfezionandi di analisi. https://www.dm.unipi.it/en/giornata-di-seminari-dei-dottorandi-e-perfeziona… Vi copio schedule, titoli e abstract. Un caro saluto, Alessandra Mercoledì 29 marzo 2023 Mattina: Aula Magna – Dipartimento di Matematica 9:00-9:45 Lorenzo Ferreri Asymptotic properties of an optimal principal eigenvalue with dirichlet boundary conditions 9:45-10:30 Michele Caselli Non-local approximation of minimal surfaces and existence of infinitely many minimal surfaces in 3-manifolds 11:00-11:45 Daniele Barbera L^p-L^q Maximal Regularity estimate for the Beris-Edward model in the half-plane 11:45-12:30 Mattia Freguglia Alcuni problemi riguardanti l’approssimazione diffusa del funzionale elastica Pomeriggio: Aula Fermi – Scuola Normale Superiore 14:00-14:45 Claudio Afeltra TBA 14:45-15:30 Camillo Brena Introduzione agli spazi RCD 16:00-16:45 Nicola Picenni How to recognize constant functions through nonlocal functionals Daniele Barbera (UNIPI) L^p-L^q Maximal Regularity estimate for the Beris-Edward model in the half-plane In this seminar we will consider the Beris-Edward model for the study of nematic liquid crystals in the half-plane R^N_+ with N\ge 2. Using the L^p-L^q Maximal Regularity Theory, we will prove the existence and uniqueness of a solution for the resolvent system and the corresponding existence and uniqueness of the solution for the linear evolution problem for p,q\in(1,\infty). As an application, we will see the existence of a local solution for the general model for small initial data for p>2 and q>N. Camillo Brena (SNS) Introduzione agli spazi RCD Lo scopo di questo seminario è di introdurre brevemente gli spazi RCD. Inizierò con un esempio che motiva l’interesse verso l’analisi in ambiente non-liscio per poi definire gli spazi RCD ed esporne le proprietà più rilevanti Michele Caselli (SNS) Non-local approximation of minimal surfaces and existence of infinitely many minimal surfaces in 3-manifolds In this talk, I will describe a possible path towards a proof of Yau's conjecture (on the existence of infinitely many minimal surfaces in every Riemannian 3-manifold) based on nonlocal approximation of minimal surfaces. On one hand, in a work in preparation with J. Serra and E. F. Simon, we show that the analog of Yau's conjecture for nonlocal minimal surfaces holds. This is because Morse theory for nonlocal minimal surfaces seems to be flawless as finite-dimensional Morse theory, at least from the compactness perspective. On the other hand, in a recent work by H. Chang, S. Dipierro, J. Serra, and E. Valdinoci the authors prove that one can successfully pass nonlocal minimal surfaces to the limit to obtain classical minimal surfaces, keeping strong curvature and separation estimates. These two works seem to point to the fact that one could recover Yau's conjecture from its nonlocal analog. Lorenzo Ferreri (SNS) Asymptotic properties of an optimal principal eigenvalue with dirichlet boundary conditions We consider a weighted eigenvalue problem for the Dirichlet laplacian in a smooth bounded domain Ω ⊂ R^N , where the bang-bang weight equals a positive constant m on the favourable region E ⊂ Ω and a negative constant −m on Ω \ E. The corresponding positive principal eigenvalue provides a threshold to detect persis- tence/extinction of a species whose evolution is described by the heterogeneous Fisher-KPP equation in population dynamics. In particular, we study the minimization of such eigen- value with respect to the shape and position of E in Ω. We provide a sharp asymptotic expansion of the optimal principal positive eigenvalue and a sharp spherical asymmetry estimate of the optimal favourable regions in the singularly perturbed regime in which the volume of E vanishes. In particular, we deduce that, up to subsequences, the optimal regions E concentrate at a point maximizing the distance from ∂Ω. This is a joint work with Gianmaria Verzini Mattia Freguglia (SNS) Alcuni problemi riguardanti l’approssimazione diffusa del funzionale elastica In questo seminario parlerò di una congettura proposta da Bellettini e Paolini come variante di una congettura precedente di De Giorgi sulla possibilità di approssimare, nel senso della Gamma-convergenza, in modo diffuso la somma del funzionale Perimetro e del funzionale di Willmore su insiemi con bordo di classe C^2. Questo problema è stato risolto da Röger e Schätzle in dimensione n=2,3 e indipendentemente da Nagase e Tonegawa in dimensione n=2, ma rimane aperto in dimensione più alta. Dopo aver introdotto il problema mi concentrerò sul caso n=2 e discuterò le difficoltà che emergono provando a estendere il risultato a insiemi meno regolari. Alla fine proporrò un possibile candidato a essere il Gamma-limite dei funzionali diffusi su tutto L^1 spiegando quali sarebbero gli step mancanti per ottenere una dimostrazione. Nicola Picenni (SNS) How to recognize constant functions through nonlocal functionals We describe a problem proposed by H. Brezis concerning the characterization of constant functions through double integrals that involve their difference quotients. In particular, we focus on the problem of finding necessary and sufficient conditions under which such characterization holds true. We present and motivate a natural necessary condition proposed by R. Ignat and we show with a counterexample that it is not sufficient. On the other hand, we describe some additional conditions under which the answer to the question turns out to be postive. Finally, we discuss many intermediate cases that remain open, and how they motivate further questions in measure theory. Some parts of the talk are based on a joint work with M. Gobbino.

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International Conference on Partial Differential Equations and Applications in honor of the 70th birthday of Pierangelo Marcati
by Luigi Forcella 17 Mar '23

17 Mar '23

Buon pomeriggio a tutte e a tutti, Inoltro il seguente annuncio di una conferenza che si terrà a L’Aquila nei giorni 19-23 Giugno 2023, e che abbiamo organizzato in occasione dei 70 anni del Professor Pierangelo Marcati. Luigi. --------------- Dear colleagues, we are pleased to announce the “International Conference on Partial Differential Equations and Applications in honor of the 70thbirthday of Pierangelo Marcati”, which will be held at the GSSI - Gran Sasso Science Institute, L’Aquila (Italy) in the period 19-23/06/2023. The conference is in honor of our dear friend and colleague Pierangelo Marcati for his 70th birthday and aims at celebrating his scientific contributions and his constant commitment to the academic community. The aim of the meeting is to gather leading experts and researchers to propose and discuss new ideas in the field of Partial Differential Equations and their applications. The list of confirmed speakers, as well as other relevant information, may be found in the webpage of the conference: https://indico.gssi.it/event/486/<https://es.sonicurlprotection-fra.com/click?PV=2&MSGID=20230317120236016256…>. Registration is free, but mandatory, and it is now open. The deadline for registering to the school is Sunday, June 4th 2023. Best regards, Debora Amadori (UnivAQ), Paolo Antonelli (GSSI), Marco Di Francesco (UnivAQ), Federica Di Michele (INGV), Donatella Donatelli (UnivAQ), Luigi Forcella (UniPi), Corrado Lattanzio (UnivAQ), Michele Palladino (UnivAQ), Bruno Rubino, (UnivAQ), Stefano Spirito (UnivAQ) ==== Apologies for multiple posting ==== ----------- Luigi Forcella, Assistant Professor (RTD-B, tenure-track) University of Pisa Department of Mathematics Largo Bruno Pontecorvo 5 57127 Pisa, Italy https://pagine.dm.unipi.it/forcella/index.html

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annullamento Colloquium Carlos Kenig
by Maria Stella Gelli 12 Mar '23

12 Mar '23

Cari tutti, purtroppo il Colloquium di Carlos Kenig previsto per martedi' prossimo alle ore 17 non si potrà tenere dato che lo speaker non potrà raggiungere Pisa come previsto a causa di uno sciopero delle compagnie aeree che partono da Berlino. Tenteremo di riproporre appena possibile il seminario previsto ma dati i numerosi impegni del Prof. Kenig ciò potrebbe non avvenire in tempi brevi. Cari saluti Maria Stella Gelli (a nome anche di Paola Boito e Francesco Sala)

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due seminari
by Alessandra Pluda 05 Mar '23

05 Mar '23

Cari tutti, vi ricordo dei due seminari dell'8 e 9 marzo. Mercoledì 8 marzo, nell'ambito dei seminari VAREG, abbiamo Damià Torres (UAB) Optimal regularity for supercritical parabolic obstacle problems https://www.dm.unipi.it/eventi/optimal-regularity-for-supercritical-parabol… ore 18:00 Aula Magna Invece Giovedì 9 marzo ci sarà un seminario di Analisi di Tohru Ozawa (Waseda) Proof of Sobolev and related inequalities via heat semigroup https://www.dm.unipi.it/eventi/?yy=2023&mm=3&dd=9 ore 17:00 Sala Seminari. A presto, Alessandra

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Prossimi seminari
by Alessandra Pluda 24 Feb '23

24 Feb '23

Cari tutti, vi mando una mail riassuntiva con la lista dei prossimi seminari del prossimo semestre organizzati finora. Un caro saluto, Alessandra 1 marzo (seminario Vareg) ore 18:00 Aula Magna Speaker: Seongmin Jeon (KTH Royal Institute of Technology) 8 marzo (seminario Vareg) ore 18:00 Aula Magna Speaker: Damià Torres (UAB) 14 marzo (Colloquium di Analisi) ore 15:30 Aula Magna Speaker: Carlos Kenig (Chicago) 22 marzo (Seminario di Analisi - PRA GeoDom) ore 17:00 Aula Seminari Speaker: Francesca Prinari (Unipi) 28 marzo Workshop Vareg "Calculus of variations and free boundary problems V" Speakers: Elisa Affili, Francesca Bianchi, Gabriele Cora, Giovanni Siclari, Stefano Vita 5 aprile (Seminario Vareg) ore 17:00 Aula Seminari Speaker: Roberto Ognibene 21 Aprile (Seminario di Analisi) ore 16:30 Aula Seminari Speaker: Filip Rindler 26 aprile: SLOT LIBERO 4 maggio (Seminario di Analisi - PRA GeoDom) Speaker: Lorenzo Brasco + Rustum Choksi (Seminario di Analisi)

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Prossimo seminari di analisi
by Alessandra Pluda 23 Jan '23

23 Jan '23

Buon giorno a tutti, mercoledì alle ore 17 in Aula Seminari avremo il prossimo seminario di Analisi: https://www.dm.unipi.it/eventi/nikodym-type-spherical-maximal-functions-ala… SPEAKER: Alan Chang, Princeton University TITLE: Nikodym-type spherical maximal functions ABSTRACT: We study L^p bounds on Nikodym maximal functions associated to spheres. In contrast to the spherical maximal functions studied by Stein and Bourgain, our maximal functions are uncentered: for each point in R^n, we take the supremum over a family of spheres containing that point. A presto J. Bellazzini, M.S. Gelli, A. Pluda

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[Indico] Carlo Gasparetto, A short proof of Allard's theorem, 06/12/2022, 17:00 Europe/Rome
by maria.stella.gelli＠unipi.it 06 Dec '22

06 Dec '22

Title: A short proof of Allard's theorem, Speaker(s): Carlo Gasparetto, SISSA, Date and time: 6 Dec 2022, 17:00 (Europe/Rome), Lecture series: Analysis Seminar, Venue: Dipartimento di Matematica (Aula Magna). You can access the full event here: https://events.dm.unipi.it/e/141 Abstract -------- Abstract. Allard's theorem roughly states that a minimal surface, that is close enough to a plane, coincides with the graph of a smooth function which enjoys suitable a priori estimates. In this talk we will show how one can prove this result by exploiting viscosity technique and a weighted monotonicity formula. This talk is based on a joint work with Guido De Philippis and Felix Schulze. -- Indico :: Email Notifier https://events.dm.unipi.it/e/141

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[Indico] Prof. Juan Casado Diaz, The influence of a strong oscillating magnetic field in an elastic body, 11/29/22, 5:00 PM Europe/Rome
by maria.stella.gelli＠unipi.it 28 Nov '22

28 Nov '22

Title: The influence of a strong oscillating magnetic field in an elastic body, Speaker(s): Prof. Juan Casado Diaz, Universidad de Sevilla, Date and time: Nov 29, 2022, 5:00 PM (Europe/Rome), Lecture series: Analysis Seminar, Venue: Dipartimento di Matematica (Sala Seminari). You can access the full event here: https://events.dm.unipi.it/e/137 Note ---- Dear all, note that tomorrow, immediately after the seminar by Casado-Diaz scheduled for 17.00, in Sala Seminari there will be the seminar by Cruz Blanquez (scheduled for 18.00). For more details have a look at the site https://www.dm.unipi.it/eventi/clustering-solutions-for-a-boundary-yamabe-p… -- Indico :: Email Notifier https://events.dm.unipi.it/e/137

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seminario di Analisi, ore 17
by Alessandra Pluda 21 Nov '22

21 Nov '22

Salve a tutti, domani martedì 22 novembre alle ore 17 ci sarà un seminario di Analisi di Gian Maria Dall'Ara (SNS Pisa). Titolo: "Old and new questions in the regularity theory of the d-bar-Neumann problem" Abstract: In this talk, I will discuss various questions in the analysis of the d-bar-Neumann problem, a classical noncoercive boundary value problem for the Laplacian whose regularity theory is of great importance in complex analysis and geometry. Despite the deep results established in the last 60 years (starting with seminal work by D. Spencer, J. J. Kohn, J. Nirenberg, E. Stein, C. Fefferman,...), several central questions remain unanswered. I will survey the field and comment on recent developments, in particular on my joint work with S. Mongodi (Università Milano-Bicocca). Ho notato solo ora che ho inserito troppo tardi il seminario sulla pagina del dipartimento e quindi non appare nel notiziario di venerdì, mi scuso dell'inconveniente. Saluti, Alessandra

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[Indico] Prof. Idriss Mazari, Existence of optimal shapes in optimal control theory, 10/18/22, 5:00 PM Europe/Rome
by maria.stella.gelli＠unipi.it 18 Oct '22

18 Oct '22

Title: Existence of optimal shapes in optimal control theory, Speaker(s): Prof. Idriss Mazari, Université de Paris Dauphine, Date and time: Oct 18, 2022, 5:00 PM (Europe/Rome), Lecture series: Analysis Seminar, Venue: Dipartimento di Matematica (Sala Riunioni). You can access the full event here: https://events.dm.unipi.it/e/119 -- Indico :: Email Notifier https://events.dm.unipi.it/e/119

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[Indico] Prof. Idriss Mazary, Existence of optimal shapes in optimal control theory, 18/10/2022, 17:00 Europe/Rome
by maria.stella.gelli＠unipi.it 13 Oct '22

13 Oct '22

Title: Existence of optimal shapes in optimal control theory, Speaker(s): Prof. Idriss Mazary, Université de Paris Dauphine, Date and time: 18 Oct 2022, 17:00 (Europe/Rome), Lecture series: Analysis Seminar, Venue: Dipartimento di Matematica (Sala Riunioni). You can access the full event here: https://events.dm.unipi.it/e/119 -- Indico :: Email Notifier https://events.dm.unipi.it/e/119

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[Indico] Prof. Idriss Mazary, Existence of optimal shapes in optimal control theory, 10/18/22, 5:00 PM Europe/Rome
by maria.stella.gelli＠unipi.it 11 Oct '22

11 Oct '22

Title: Existence of optimal shapes in optimal control theory, Speaker(s): Prof. Idriss Mazary, Université de Paris Dauphine, Date and time: Oct 18, 2022, 5:00 PM (Europe/Rome), Lecture series: Analysis Seminar, Venue: Dipartimento di Matematica (Sala Seminari). You can access the full event here: https://events.dm.unipi.it/e/119 Abstract -------- In this talk, we present several recent contributions (in collaboration with G. Nadin and Y. Privat) on the question of the existence of optimal shapes in optimal control theory for bilinear models. Motivated by applications in spatial ecology, we investigate the following problem: consider a parabolic or elliptic equation$Lu=mu+F(u)$ where $L$ is a parabolic or elliptic operator, $m$ is the control and $F$ is a given non-linearity. The goal is to solve the optimisation problem$$Max_m \int_\Omega j(x;u)\,dx$$where $j$ is simply a cost functional, and $m$ is an admissible control that satisfies $L^1$ and $L^\infty$ bounds. In other words, we assume $0\le m\le1$ almost everywhere, and $\int_\Omega m\,dx=V_0$ where $V_0$ is a fixed volume constraint. A basic property for such problem is to obtain the bang-bang property for maximisers. In other words, are optimal control characteristic functions of subsets of the domain on which the equation is set? Put otherwise, can optimisers be identified with subsets of the domain? What we explain in this talk is that for bilinear control problems, the answer is analogous to the Buttazzo-DalMaso theorem: if the functional we want to optimise is monotonic, then the answer to this question is positive. Our result relies on new oscillatory techniques. Note ---- Il seminario di martedi' 18 ottobre si terrà in sala Riunioni invece che in Sala Seminari a causa della concomitanza con un Meeting Erasmus già programmato in Sala Seminari -- Indico :: Email Notifier https://events.dm.unipi.it/e/119

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[Indico] Gaetano Siciliano, Critical points at prescribed energy levels, 10/10/22, 5:00 PM Europe/Rome
by maria.stella.gelli＠unipi.it 10 Oct '22

10 Oct '22

Title: Critical points at prescribed energy levels, Speaker(s): Gaetano Siciliano, Univ. San Paulo, Br, Date and time: Oct 10, 2022, 5:00 PM (Europe/Rome), Lecture series: Analysis Seminar, Venue: Dipartimento di Matematica (Sala Seminari). You can access the full event here: https://events.dm.unipi.it/e/121 Abstract -------- In this talk, we discuss the existence of critical points for a family of abstract and smooth functionals on Banach spaces under the energy constraint. By using the Ljusternick-Schnirelmann theory and the fibering method of Pohozaev we show, under suitable assumptions, multiplicity results.The abstract framework is then applied to some partial differential equations depending on a parameter for which we obtain multiple solutions as well as some bifurcation results. -- Indico :: Email Notifier https://events.dm.unipi.it/e/121

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[Indico] Elia Bruè, Non-uniqueness of Leray solutions of the forced Navier-Stokes equations, 28/06/2022, 16:30 Europe/Rome
by maria.stella.gelli＠unipi.it 03 Oct '22

03 Oct '22

Title: Non-uniqueness of Leray solutions of the forced Navier-Stokes equations, Speaker(s): Elia Bruè, Institute for Advanced Study (Princeton), Date and time: 28 Jun 2022, 16:30 (Europe/Rome), Lecture series: Analysis Seminar, Venue: Dipartimento di Matematica (Aula Magna). You can access the full event here: https://events.dm.unipi.it/e/100 Abstract -------- In his seminal work, Leray demonstrated the existence of global weak solutions, with nonincreasing energy, to the Navier-Stokes equations in three dimensions. In this talk, we exhibit two distinct Leray solutions with zero initial velocity and identical body force. Building on a recent work of Vishik, we construct a linear unstable self-similar solution to the 3D Navier-Stokes with force. We employ the linear instability of the latter to build the second solution, which is a trajectory on the unstable manifold, in accordance with the predictions of Jia and Šverák. -- Indico :: Email Notifier https://events.dm.unipi.it/e/100

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[Indico] Carlo Mantegazza , The Riemannian Penrose inequality via nonlinear potential theory, 11/07/2022, 17:30 Europe/Rome
by maria.stella.gelli＠unipi.it 11 Jul '22

11 Jul '22

Title: The Riemannian Penrose inequality via nonlinear potential theory, Speaker(s): Carlo Mantegazza , Università di Napoli, Date and time: 11 Jul 2022, 17:30 (Europe/Rome), Lecture series: Analysis Seminar, Venue: Dipartimento di Matematica (Aula Magna). You can access the full event here: https://events.dm.unipi.it/e/101 Abstract -------- We will discuss the Riemannian Penrose inequality in an asymptotically flat 3-manifold with nonnegative scalar curvature and the main points of a new proof by means of a monotonicity formula holding along the level sets of the p-capacitary potentials of the horizon boundary. Joint work with Virginia Agostiniani, Lorenzo Mazzieri and Francesca Oronzio. -- Indico :: Email Notifier https://events.dm.unipi.it/e/101

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[Indico] Carlo Mantegazza , The Riemannian Penrose inequality via nonlinear potential theory, 7/11/22, 5:30 PM Europe/Rome
by maria.stella.gelli＠unipi.it 07 Jul '22

07 Jul '22

Title: The Riemannian Penrose inequality via nonlinear potential theory, Speaker(s): Carlo Mantegazza , Università di Napoli, Date and time: Jul 11, 2022, 5:30 PM (Europe/Rome), Lecture series: Analysis Seminar, Venue: Dipartimento di Matematica (Aula Magna). You can access the full event here: https://events.dm.unipi.it/e/101 Abstract -------- We will discuss the Riemannian Penrose inequality in an asymptotically flat 3-manifold with nonnegative scalar curvature and the main points of a new proof by means of a monotonicity formula holding along the level sets of the p-capacitary potentials of the horizon boundary. Joint work with Virginia Agostiniani, Lorenzo Mazzieri and Francesca Oronzio. Note ---- Note the change of title and abstract!!! Time and location are the same -- Indico :: Email Notifier https://events.dm.unipi.it/e/101

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[Indico] Carlo Mantegazza , Li & Yau estimates for some semilinear heat equations, 11/07/2022, 17:30 Europe/Rome
by maria.stella.gelli＠unipi.it 07 Jul '22

07 Jul '22

Title: Li & Yau estimates for some semilinear heat equations, Speaker(s): Carlo Mantegazza , Università di Napoli, Date and time: 11 Jul 2022, 17:30 (Europe/Rome), Lecture series: Analysis Seminar, Venue: Dipartimento di Matematica (Aula Magna). You can access the full event here: https://events.dm.unipi.it/e/101 Abstract -------- We will show some Li & Yau–type gradient estimates for positive solutions of the semilinear heat equations $u_t =\Delta u + u^p$ with p>1, on a complete n–dimensional Riemannian manifold (M,g) with nonnegative Ricci tensor. We then discuss some applications to ancient and eternal solutions. Joint work with Giacomo Ascione, Daniele Castorina and Giovanni Catino. -- Indico :: Email Notifier https://events.dm.unipi.it/e/101

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[Indico] Elia Bruè, Non-uniqueness of Leray solutions of the forced Navier-Stokes equations, 28/06/2022, 16:30 Europe/Rome
by maria.stella.gelli＠unipi.it 23 Jun '22

23 Jun '22

Title: Non-uniqueness of Leray solutions of the forced Navier-Stokes equations, Speaker(s): Elia Bruè, Institute for Advanced Study (Princeton), Date and time: 28 Jun 2022, 16:30 (Europe/Rome), Lecture series: Analysis Seminar, Venue: Dipartimento di Matematica (Aula Magna). You can access the full event here: https://events.dm.unipi.it/e/100 Abstract -------- In his seminal work, Leray demonstrated the existence of global weak solutions, with nonincreasing energy, to the Navier-Stokes equations in three dimensions. In this talk, we exhibit two distinct Leray solutions with zero initial velocity and identical body force. Building on a recent work of Vishik, we construct a linear unstable self-similar solution to the 3D Navier-Stokes with force. We employ the linear instability of the latter to build the second solution, which is a trajectory on the unstable manifold, in accordance with the predictions of Jia and Šverák. -- Indico :: Email Notifier https://events.dm.unipi.it/e/100

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[Indico] Prof. Eduard Feireisl, Long time behavior of solutions to open fluid systems, 25/05/2022, 17:00 Europe/Rome
by maria.stella.gelli＠unipi.it 25 May '22

25 May '22

Title: Long time behavior of solutions to open fluid systems, Speaker(s): Prof. Eduard Feireisl, Institute of Mathematics, Czech Academy of Sciences, Date and time: 25 May 2022, 17:00 (Europe/Rome), Lecture series: Analysis Seminar, Venue: room Sala Seminari. You can access the full event here: https://events.dm.unipi.it/e/93 Abstract -------- We consider the physically relevant fully compressible setting of the Rayleigh-Benard problem of a fluid confined between two parallel plates, heated from the bottom, and subjected to the gravitational force. Under suitable restrictions imposed on the constitutive relations we show that this open system is dissipative in the sense of Levinson, meaning there exists a bounded absorbing set for any global-in-time weak solution. In addition, global-in-time trajectories are asymptotically compact in suitable topologies and the system possesses a global compact trajectory attractor. The standard technique of Krylov and Bogolyubov then yields the existence of an invariant measure - a stationary statistical solution sitting on the global attractor. In addition, the Birkhoff--Khinchin ergodic theorem provides convergence of ergodic averages of solutions belonging to the attractor a.s. with respect to the invariant measure. -- Indico :: Email Notifier https://events.dm.unipi.it/e/93

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[Indico] Salvatore Stuvard, Existence of canonical multi-phase Brakke flows-VAREG seminar, 25/05/2022, 16:00 Europe/Rome
by maria.stella.gelli＠unipi.it 25 May '22

25 May '22

Title: Existence of canonical multi-phase Brakke flows-VAREG seminar, Speaker(s): Salvatore Stuvard, Università degli Studi di Milano, Date and time: 25 May 2022, 16:00 (Europe/Rome), Lecture series: Analysis Seminar, Venue: room Sala Seminari. You can access the full event here: https://events.dm.unipi.it/e/94 Abstract -------- VAREG-Seminar -Abstract -- Indico :: Email Notifier https://events.dm.unipi.it/e/94

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[Indico] Salvatore Stuvard, Existence of canonical multi-phase Brakke flows-VAREG seminar, 25/05/2022, 16:00 Europe/Rome
by maria.stella.gelli＠unipi.it 23 May '22

23 May '22

Title: Existence of canonical multi-phase Brakke flows-VAREG seminar, Speaker(s): Salvatore Stuvard, Università degli Studi di Milano, Date and time: 25 May 2022, 16:00 (Europe/Rome), Lecture series: Analysis Seminar, Venue: room Sala Seminari. You can access the full event here: https://events.dm.unipi.it/e/94 Abstract -------- VAREG-Seminar -Abstract -- Indico :: Email Notifier https://events.dm.unipi.it/e/94

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[Indico] Prof. Eduard Feireisl, Long time behavior of solutions to open fluid systems, 25/05/2022, 17:00 Europe/Rome
by maria.stella.gelli＠unipi.it 23 May '22

23 May '22

Title: Long time behavior of solutions to open fluid systems, Speaker(s): Prof. Eduard Feireisl, Institute of Mathematics, Czech Academy of Sciences, Date and time: 25 May 2022, 17:00 (Europe/Rome), Lecture series: Analysis Seminar, Venue: room Sala Seminari. You can access the full event here: https://events.dm.unipi.it/e/93 Abstract -------- Abstract. -- Indico :: Email Notifier https://events.dm.unipi.it/e/93

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