October 2024 - Analysis-seminar - Mailing list — Dipartimento di Matematica, UniPI

Reminder seminario domani giovedì 31 ottobre
by Ilaria Lucardesi 30 Oct '24

30 Oct '24

Care tutte e cari tutti, Ricordiamo il seminario di domani, giovedì 31 ottobre, alle 17 in Sala Seminari, "Evolution of gaussian fields by the flow of the nonlinear Schrödinger equation" di Nikolay Tzvetkov (École Normale Supérieure de Lyon). Trovate l'abstract qui sotto. Attenzione all'aula, diversa dal solito. A presto, Ilaria Lucardesi e Luigi Forcella. ---------------------------------------------------------- Deal all, We remind you the seminar "Evolution of gaussian fields by the flow of the nonlinear Schrödinger equation" by Nikolay Tzvetkov (École Normale Supérieure de Lyon), tomorrow, thursday 31st october, at 5p.m. in Sala Seminari. Pay attention to the room: it is not the usual one! Please, find the abstract here below. Best wishes, Ilaria Lucardesi e Luigi Forcella. ---------------------------------------------------------- Speaker: Nikolay Tzvetkov (École Normale Supérieure de Lyon) Title: Evolution of gaussian fields by the flow of the nonlinear Schrödinger equation Abstract: We will discuss the non linear Schrödinger equation with data distributed according to gaussian fields. These fields are invariant under the free evolution and the question is how much the non linear interaction affects the invariance property. We will present a recent result, obtained in collaboration with Chenmin Sun, showing that for the three dimensional energy critical problem the law of the solution at any time is absolutely continuous with respect to the law of the initial gaussian field. We are therefore in slightly out of equilibrium regime. It should be emphasized that, thanks to the work by Aizenman and Duminil-Copin, we do not expect to reasonably define a Gibbs measure for an energy critical problem. Therefore the consideration of general gaussian fields becomes even more natural. The main new idea is the use of a cancellation of (probabilistically) resonant contributions in a modified energy estimate. We also rely on several techniques developed in recent years in the field of probabilistic well-posedness of dispersive PDE's. We will overview these ideas and techniques.

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Reminder seminario analisi domani
by Luigi Forcella 16 Oct '24

16 Oct '24

Care tutte e cari tutti, Ricordiamo il seminario<https://www.dm.unipi.it/en/seminar/?id=66e05134ed270fad8e15eaf7> di domani alle 17 in Aula Riunioni “Dynamics of the 3D Navier-Stokes equations from initial data with zero third component” di T. Barker (Bath). Il seminario sarà preceduto da uno snack alle 16:45 nella stessa aula. A presto, Ilaria Lucardesi e Luigi Forcella. ---------------------------------------------------------- Deal all, We remind you the seminar<https://www.dm.unipi.it/en/seminar/?id=66e05134ed270fad8e15eaf7> “Dynamics of the 3D Navier-Stokes equations from initial data with zero third component” by T. Barker (Bath), tomorrow at 5p.m. in Aula Riunioni. There will be a snack at 4:45 pm in the same room. Best wishes, Ilaria Lucardesi e Luigi Forcella. ----------- 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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Reminder seminari Analisi oggi e domani
by Luigi Forcella 10 Oct '24

10 Oct '24

Care tutte e cari tutti, Ricordiamo il seminario<https://www.dm.unipi.it/en/seminar/?id=66fe659042845121abe48caf> di oggi alle 17 in Aula Riunioni “A finite element approximation of a simplified model for smart fluids: an error analysis” di A. Kaltenbach (TUB). Ricordiamo inoltre il seminario<https://www.dm.unipi.it/en/seminar/?id=66fe7a4342845121abe491c1> che si terrà domani alle 17 in Aula Riunioni “Alberti representations, rectifiability and regularity of measures satisfying a PDE” di D. Bate (Warwick) La prossima settimana il seminario di Analisi sarà giovedì con speaker T. Barker (Bath). Seguirà annuncio. Ilaria Lucardesi e Luigi Forcella. ————— Deal all, We remind you the seminar “A finite element approximation of a simplified model for smart fluids: an error analysis” by A. Kaltenbach (TUB), today at 5p.m. in Aula Riunioni. We also remind you the seminar “Alberti representations, rectifiability and regularity of measures satisfying a PDE” by D. Bate (Warwick), tomorrow at 5p.m. in Aual Riunioni. The next seminar will be next Thursday, and the speaker will be T. Barker (Bath). We will announce it tomorrow. Best regards, Ilaria Lucardesi e Luigi Forcella. ----------- 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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Annuncio seminari Analisi 9 e 10 ottobre 2024
by Luigi Forcella 03 Oct '24

03 Oct '24

Care tutte, cari tutti, La settimana prossima avremo due eventi per il ciclo dei Seminari di Analisi: • Mercoledì 9 ottobre, ore 17, avremo il piacere di ascoltare Alex Kaltenbach (TUB), che terrà un seminario dal titolo “A finite element approximation of a simplified model for smart fluids: an error analysis" • Giovedì 10 ottobre, ore 17, avremo il piacere di ascoltare David Bate (Warwick), che terrà un seminario dal titolo “Alberti representations, rectifiability and regularity of measures satisfying a PDE”. Trovate sotto gli abstract. Ricordiamo anche che oggi alle 17 in Aula Riunioni ci sarà il seminario di Chiara Boccato (UniPi), preceduto da uno snack nella stessa aula alle 16:45. A presto, Ilaria Lucardesi e Luigi Forcella ____ Dear all, The next week we will have two events for the Mathematical Analysis Seminars: • Wednesday 9 October, 5PM, we will have the pleasure of listening to Alex Kaltenbach (TUB).The title of the talk is “A finite element approximation of a simplified model for smart fluids: an error analysis”. • Thursday 10 October, 5PM, we will have the pleasure of listening to David Bate (Warwick).The title of the talk is “Alberti representations, rectifiability and regularity of measures satisfying a PDE”. Below the abstracts. We remind that today at 5PM there will be the seminar by Chiara Boccato (UniPi) in Aula Riunioni, with a snack in the same room at 4:45 pm. Best regards, Ilaria Lucardesi and Luigi Forcella. ——————— Speaker: Alex Kaltenbach Title: A finite element approximation of a simplified model for smart fluids: an error analysis Abstract: In this talk, a finite element approximation of the steady p(⋅)p(⋅)-Navier-Stokes equations (p(⋅)p(⋅) is variable dependent) is examined for orders of convergence by assuming natural fractional regularity assumptions on the velocity vector field and the kinematic pressure. Numerical experiments confirm the quasi-optimality of the apriori error estimates (for the velocity). The steady p(⋅)p(⋅)-Navier-Stokes equations are a prototypical example of a non-linear system with variable growth conditions. They appear naturally in physical models for so-called smart fluids,e.g., electro-rheological fluids, micro-polar electro-rheological fluids, magneto-rheological fluids, chemically reacting fluids, and thermo-rheological fluids, and have the potential for an application in numerous areas, e.g., in electronic, automobile, heavy machinery, military, and biomedical industry. Speaker: David Bate. Title: Alberti representations, rectifiability and regularity of measures satisfying a PDE Abstract: An Alberti representation of a (finite, Borel) measure is a decomposition into 1-rectifiable measures. By Fubini's theorem, Lebesgue measure on [0,1]^n has n "independent" Alberti representations, each one consisting of curves parallel to a coordinate axis. This naturally extends to representations of n-rectifiable sets in Euclidean space, where the tangents to curves span the approximate tangent space almost everywhere, and can be extended further to rectifiable subsets of a metric space. This talk will consider the converse statement. We will show that, if n-dimensional Hausdorff measure of a metric space X has n independent Alberti representations, then X is n-rectifiable. This result has numerous applications to rectifiability in metric spaces that will be discussed. We will also discuss a key element of the proof on the integrability of measuressatisfying a PDE constraint. This talk is based on joint work with Tuomas Orponen and Julian Weigt. ----------- 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 ----------- 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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