Institut Élie Cartan de Lorraine

About: Institut Élie Cartan de Lorraine is a facility organization based out in Vandœuvre-lès-Nancy, France. It is known for research contribution in the topics: Boundary value problem & Stochastic differential equation. The organization has 345 authors who have published 1084 publications receiving 15512 citations. The organization is also known as: Institut Élie-Cartan de Nancy.

Existence of strong solutions for a system of interaction between a compressible viscous fluid and a wave equation

Abstract: In this article, we consider a fluid-structure interaction system where the fluid is viscous and compressible and where the structure is a part of the boundary of the fluid domain and is deformable. The fluid is governed by the barotropic compressible Navier-Stokes system whereas the structure displacement is described by a wave equation. We show that the corresponding coupled system admits a unique strong solution for an initial fluid density and an initial fluid velocity in $H^3$ and for an initial deformation and an initial deformation velocity in $H^4$ and $H^3$ respectively. The reference configuration for the fluid domain is a rectangular cuboid with the elastic structure being the top face. We use a modified Lagrangian change of variables to transform the moving fluid domain into the rectangular cuboid and then analyze the corresponding linear system coupling a transport equation (for the density), a heat-type equation, and a wave equation. The corresponding results for this linear system and estimations of the coefficients coming from the change of variables allow us to perform a fixed point argument and to prove the existence and uniqueness of strong solutions for the nonlinear system, locally in time.

Aspect conforme de l'opérateur de Dirac sur une variété à bord

Abstract: La principale motivation des travaux de cette these est d'etudier l'aspect conforme du spectre de l'operateur de Dirac sur une variete a bord. Dans un premier temps, on donnera des estimations de la premiere valeur propre de l'operateur de Dirac fondamental de la variete M sous deux conditions a bord locales prenant en compte leurs proprietes conformes. Une etude detaillee de ces conditions a bord permet alors de clore cette premiere partie par une estimation classique du spectre de l'operateur de Dirac, raffinant un resultat anterieur de O. Hijazi, S. Montiel et A. Roldan. Dans un second temps, on construit un invariant spinoriel conforme a partir de la premiere valeur propre de l'operateur de Dirac sous une des conditions a bord etudiee dans le premier chapitre. Cet invariant peut etre vu comme l'analogue de l'invariant de Yamabe dans le cadre spinoriel. Une etude approfondie de cet invariant conduit de maniere naturelle a la construction de la fonction de Green de l'operateur de Dirac.

On weak approximation of stochastic differential equations with discontinuous drift coefficient

Abstract: In this paper, weak approximations of multi-dimensional stochastic differential equations with discontinuous drift coefficients are considered. Here as the approximated process, the Euler-Maruyama approximation of SDEs with approximated drift coefficients is used, and we provide a rate of weak convergence of them. Finally we present a rate of weak convergence of the Euler-Maruyama approximation of the original SDEs with constant diffusion coefficients.

Asymptotic shape for the chemical distance and first-passage percolation in random environment

Abstract: The aim of this paper is to generalize the well-known asymptotic shape result for first-passage percolation on $\Zd$ to first-passage percolation on a random environment given by the infinite cluster of a supercritical Bernoulli percolation model. We prove the convergence of the renormalized set of wet points to a deterministic shape that does not depend on the random environment. As a special case of the previous result, we obtain an asymptotic shape theorem for the chemical distance in supercritical Bernoulli percolation. We also prove a flat edge result. Some various examples are also given.