Groupe de Travail des Thésard·e·s du LJLL

Le mercredi à 17h en salle de séminaire

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Exposés à venir :

20 décembre 2023

Trung Hieu Giang (City University of Hong Kong)
Existence theorems for nonlinear shell models of Koiter's type
Résumé

The nonlinear shell model of W. T. Koiter is a system of nonlinear partial differential equations whose solution predicts the deformation of a nonlinearly elastic shell in response to applied forces and boundary conditions. However, up to now, the minimization problem associated with this system has not been justified by an existence theorem. In this talk, under the assumption that the middle surface of the shell is a minimal surface, we approach this minimization problem by a new minimization problem that is well-posed over the same space of admissible deformations.

10 janvier 2024

Marcel Zodji (IMJ-PRG (SG))

A valider
Density-patch problem for the compressible viscous fluid with density-dependent viscosity
Résumé

The motion of a compressible viscous barotropic fluid is described by the Navier-Stokes system. It is a system of hyperbolic-parabolic mixed-type PDEs. In this talk, we will study the so-called density patch problem: If we are given a density that is initially discontinuous across a $\mathcal C^{1+\alpha}$ curve $\gamma$ and $\alpha$-H\"older continuous on the two disjoint components delimited by $\gamma$, is this structure preserved in time?
An important quantity in the mathematical analysis of this system is the so-called effective flux, which was discovered in [Hoff and Smoller, 1985]. More precisely, the mathematical properties of this quantity play a crucial role in the study of the propagation of oscillations in compressible fluids [Serre, 1991], in the construction of weak solutions [P-L Lions, 1996], or the propagation of discontinuity surfaces [Hoff, 2002], to cite just a few examples. In the case of density-dependent viscosities, the behavior of the effective flux degenerates, which renders the analysis more subtle.

7 février 2024

Pablo López Rivera (LJLL, Université Paris Cité)
Preservation of functional inequalities under log-Lipschitz perturbations
Résumé

Given a probability measure satisfying some functional inequalities (Poincaré, log-Sobolev, etc.), it is natural to wonder if these remain valid for a perturbation of the measure. In particular, if there exists a globally Lipschitz map pushing forward the source measure towards its perturbation, then it is easy to transport certain functional inequalities. For example, Caffarelli’s contraction theorem states that the optimal transport map between the Gaussian measure and a log-concave perturbation is 1-Lipschitz.

In this talk I will show how such a map exists if we consider log-Lipschitz perturbations of a measure on a Riemannian manifold, via the interpolation given by the Langevin diffusion associated to the source measure (aka Kim-Milman’s heat flow transport map), assuming as well control on the curvature of the manifold at first and second order in the sense of Bakry-Émery-Ricci.

Exposés passés :

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Le séminaire a lieu sur le site de Jussieu:

4 Place Jussieu 75005 Paris
Salle des séminaires au 3ème étage, couloir 15-16
Accès : et , station Jussieu.

Pour tout renseignement sur le GTT, contacter: Charles Elbar (charles.elbar[at]sorbonne-universite.fr), Guillaume Garnier (guillaume.garnier[at]sorbonne-universite.fr), Lucas Perrin (lucas.perrin[at]inria.fr), Ludovic Souetre (ludovic.souetre[at]sorbonne-universite.fr) et Zhe Chen(zhe.chen[at]sorbonne-universite.fr)