Didier Bresch
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Discontinuous shear-thickening asymptotic for power-law systems related to compressible flows Open
In this paper we study the convergence of a power-law model for dilatant compressible fluids to a class of models exhibiting a maximum admissible shear rate, called thick compressible fluids. These kinds of problems were studied previously…
Global weak solutions of the Navier-Stokes-Korteweg Equations in one dimension Open
We prove the global existence of weak solutions of the one-dimensional Navier-Stokes-Korteweg (NSK) equations when the viscosity and the capillarity coefficients are power functions of the density, which may be zero on a set with positive …
Two-phase averaged system justification for ideal gases without conductivity Open
This article concerns the mathematical justification of an averaged system of partial differential equations governing the evolution of a two-phase mixture of compressible ideal fluids, with viscosity and without conductivity, in space dim…
The shoreline problem for the one-dimensional shallow water and Green-Naghdi equations Open
The Green-Naghdi equations are a nonlinear dispersive perturbation of the nonlinear shallow water equations, more precise by one order of approximation. These equations are commonly used for the simulation of coastal flows, and in particul…
Note on strongly hyperbolic systems with involutive characteristics Open
We consider the Cauchy problem in L 2 for first order system. A necessary condition is that the system must be uniformly diagonaliz-able, or equivalently that it admits a bounded symmetrizer. A sufficient condition is that it admits a smoo…
On the Boyd-Kadomstev System for a three-wave coupling problem and its asymptotic limit Open
article accepted for publication in Comm Math. Physics
The Cauchy Problem for Wave Equations with NonLipschitz Coefficients Open
In this paper we study the Cauchy problem for second order strictly hyperbolic operators when the coefficients of the principal part are not Lipschitz continuous, but only “Log-Lipschitz” with respect to all the variables. This class of eq…
Do gas fluxes from numerical modeling and from field data match ? Open
Modeling magma ascent within volcanic conduits is not an easy task since it involves complex physical interactions between melt, crystals and gas. Since the evolution of gas content mainly controls the eruptive dynamics, we have to do our …
A duality method for mean-field limits with singular interactions Open
We introduce a new approach to derive mean-field limits for first- and second-order particle systems with singular interactions. It is based on a duality approach combined with the analysis of linearized dual correlations, and it allows to…
Functional inequalities and strong Lyapunov functionals for free surface flows in fluid dynamics Open
This paper is motivated by the study of Lyapunov functionals for the Hele-Shaw and Mullins-Sekerka equations describing free surface flows in fluid dynamics. We prove that the L^2 -norm of the free surface elevation and the area of the fre…
View article: Sliding and merging of strongly sheared droplets
Sliding and merging of strongly sheared droplets Open
A mathematical and numerical framework is proposed to compute the displacement and merging dynamics of sliding droplets under the action of a constant shear exerted by a gas flow. An augmented formulation is implemented to model surface te…
Mean field limit and quantitative estimates with singular attractive kernels Open
This paper proves the mean field limit and quantitative estimates for many-particle systems with singular attractive interactions between particles. As an important example, a full rigorous derivation (with quantitative estimates) of the P…
Global Existence of Weak Solutions for Compresssible Navier--Stokes--Fourier Equations with the Truncated Virial Pressure Law Open
This paper concerns the existence of global weak solutions {\it à la Leray} for compressible Navier--Stokes--Fourier systems with periodic boundary conditions and the truncated virial pressure law which is assumed to be thermodynamically u…
Global Existence of Weak Solutions for Compresssible Navier—Stokes—Fourier Equations with the Truncated Virial Pressure Law Open
This paper concerns the existence of global weak solutions á la Leray for compressible Navier–Stokes–Fourier systems with periodic boundary conditions and the truncated virial pressure law which is assumed to be thermodynamically unstable.…
The soundproof model of an acoustic--internal waves system with low stratification Open
This work is devoted to investigating a compressible fluid system with low stratification, which is driven by fast acoustic waves and internal waves. The approximation using a soundproof model is justified. More precisely, the soundproof m…
A new approach to the mean-field limit of Vlasov-Fokker-Planck equations Open
This article introduces a novel approach to the mean-field limit of stochastic systems of interacting particles, leading to the first ever derivation of the mean-field limit to the Vlasov-Poisson-Fokker-Planck system for plasmas in dimensi…
Large-time behavior of compressible polytropic fluids and nonlinear Schrödinger equation Open
In this paper we analyze the large-time behavior of weak solutions to polytropic fluid models possibly including quantum and capillary effects. Formal a priori estimates show that the density of solutions to these systems should disperse w…
Global existence of entropy-weak solutions to the compressible Navier–Stokes equations with non-linear density dependent viscosities Open
In this paper, we considerably extend the results on global existence of entropy-weak solutions to the compressible Navier–Stokes system with density dependent viscosities obtained, independently (using different strategies) by Vasseur–Yu …
A viscoelastic model for avascular tumor growth. Open
In this article, we present a continuous model for tumor growth . This model describes the evolution of three cellular densities: the density of sane tissue, cancer cells and extracellular medium. In order to render correctly the cellular …
Extension of the Hoff solutions framework to cover Navier-Stokes\n equations for a compressible fluid with anisotropic viscous-stress tensor Open
This paper deals with the Navier-Stokes system governing the evolution of a\ncompressible barotropic fluid. We extend D. Hoff's intermediate regularity\nsolutions framework by relaxing the integrability needed for the initial\ndensity whic…
Extension of the Hoff solutions framework to cover Navier-Stokes equations for a compressible fluid with anisotropic viscous-stress tensor Open
This paper deals with the Navier-Stokes system governing the evolution of a compressible barotropic fluid. We extend D. Hoff's intermediate regularity solutions framework by relaxing the integrability needed for the initial density which i…
Nonclassical multidimensional viscous and inviscid shocks Open
Extending our earlier work on Lax-type shocks of systems of conservation laws, we establish existence and stability of curved multidimensional shock fronts in the vanishing viscosity limit for general Lax- or undercompressive-type shock wa…
Uniform Stability Estimates for Constant-Coefficient Symmetric Hyperbolic Boundary Value Problems Open
Answering a question left open in [MZ2], we show for general symmetric hyperbolic boundary problems with constant coefficients, including in particular systems with characteristics of variable multiplicity, that the uniform Lopatinski cond…
On an existence theory for a fluid-beam problem encompassing possible contacts Open
In this paper we consider a coupled system of pdes modeling the interaction between a two-dimensional incompressible viscous fluid and a one-dimensional elastic beam located on the upper part of the fluid domain boundary. We design a funct…
Cpcn - Bilan De Mandature 2016 – 2021 Open
Le présent bilan de mandature 2016-2021 de la CPCN (Conférence des présidentes et présidents de sections et de commissions interdisciplinaires du Comité national de la recherche scientifique) a une triple finalité. Il constitue d'abord une…