Mon, 17 Feb 2025
16:30

L4

Stable Free Boundaries in Dimension 3: Bernoulli and Allen--Cahn

Xavier Fernandez-Real

(EPFL)

Abstract

In this talk, we present a forthcoming work on the classification of global stable solutions to the Bernoulli problem in $\mathbb R^3$. In particular, this yields local universal curvature bounds for the free boundary for the local problem.

By means of this result, we prove the free boundary Allen--Cahn stability conjecture in dimension 3: global stable solutions to the free boundary analogue of the Allen--Cahn equation are one dimensional in dimension 3. This solves a long-standing conjecture in the free boundary case.

 

Mon, 06 May 2024
16:30

L4

On Galerkin approximations of the 2D Euler equations

Luigi Berselli

(University of Pisa)

Abstract

We study fully discrete approximation of the 2D Euler equations for ideal homogeneous fluids. We focus on spectral methods and  discuss rates of convergence of velocity and vorticity under different assumptions on the smoothness of the data.

Mon, 20 May 2024
15:30

L3

Multiscale analysis of wave propagation in random media

Prof Josselin Garnier

(Centre de Mathematiques Appliquees, Ecole polytechnique, Institut Polytechnique de Paris)

Further Information

This is a joint seminar with the Stochastic Analysis & Mathematical Finance seminar.