Care tutte e cari tutti,

Questo Venerdì, 23 gennaio 2026, nell’ambito dei Seminari di Analisi, avremo il piacere di ascoltare Jule Schindler (Friedrich-Alexander-Universität Erlangen-Nürnberg), che terrà un seminario dal titolo “The Nonlocal-to-Local Limit for the Inviscid Leray-α Equations”.

Il seminario si terrà in Aula Seminari ex-DMA alle ore 16:30.

Trovate l’abstract qui sotto.

Ricordo inoltre che Mercoledì 21, ore 16 in Aula Magna, ci sarà il seminario di R. F. Horta, dal titolo “Poincaré constants, fundamental frequencies and the isoanisotropic problem”.

A presto,

Luigi

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Dear all,

On Friday, 23 January 2026, as part of the Analysis Seminar Series, we will have the pleasure of hosting Jule Schindler (Friedrich-Alexander-Universität Erlangen-Nürnberg), who will give a seminar entitled “The Nonlocal-to-Local Limit for the Inviscid Leray-α Equations”

The seminar will take place in the Aula Seminari ex-DMA at 4:30 p.m.

You will find the abstract below.

I also remind you that on Wednesday, 21 January at 4 p.m. in Aula Magna, there will be the seminar by R. F. Horta entitled “Poincaré constants, fundamental frequencies and the isoanisotropic problem”.

Best regards,

Luigi

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Speaker: Jule Schindler (Friedrich-Alexander-Universität Erlangen-Nürnberg)

Title: The Nonlocal-to-Local Limit for the Inviscid Leray-α Equations

Abstract: We consider the inviscid Leray-

α

equations -- an inviscid nonlocal regularisation of the Euler equations -- on

[0, T] \times Ω

$α$

{\begin{cases} \partial_{t} v^{α} + (u^{α} \cdot \nabla) v^{α} + \nabla p^{α} = 0, \\ v^{α} = u^{α} - α^{2} Δ u^{α}, \\ div v^{α} = div u^{α} = 0, \\ v^{α} (0, \cdot) = v_{0}^{α}, \end{cases}

with $Ω \subset R^{d}$ , $d = 2, 3$ . On bounded domains, we impose the boundary condition

u^{α} = 0 on \partial Ω .

In the first part, we prove the convergence of strong solutions of the Leray-a equations to strong solutions of the Euler equations in $H^{s} (R^{d}), s > d / 2 + 1$ , for a large class of regularising kernels. In the second part, we conslder weak solutions on a bounded domain with a local scaling property far away from the boundary. The scaling relates to second-order structure functions from turbulence theory and does not imply regularity. Nonetbeless, under these assumptions, the weak solutions converge to (possibly wild) weak solutions of Euler in $L^{2}$ for a.e. $t$ .

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Luigi Forcella, Associate Professor
University of Pisa
Department of Mathematics
Largo Bruno Pontecorvo 5
57127 Pisa, Italy

https://pagine.dm.unipi.it/forcella/index.html