159 citations · 747 across the 28 of their papers we have counts for
33 papers
Propagation of chaos for the homogeneous Boltzmann equation with moderately soft potentials
Nicolas Fournier, Stéphane Mischler
We show that the Kac particle system converges, as the number of particles tends to infinity, to the solution of the homogeneous Boltzmann equation, in the regime of moderately sof…
The Landau equation in a domain
Kleber Carrapatoso, Stéphane Mischler
This work deals with the Landau equation in a bounded domain with the Maxwell reflection condition on the boundary for any (possibly smoothly position dependent) accommodation coef…
The Kinetic Fokker-Planck equation in a domain: Ultracontractivity, hypocoercivity and long-time asymptotic behavior
Kleber Carrapatoso, Stéphane Mischler
We consider the Kinetic Fokker-Planck (FKP) equation in a domain with Maxwell reflection condition on the boundary. We establish the ultracontractivity of the associated semigroup…
On the self-similar stability of the parabolic-parabolic Keller-Segel equation
Frank Alvarez Borges, Kleber Carrapatoso, Stéphane Mischler
We consider the parabolic-parabolic Keller-Segel equation in the plane and prove the nonlinear exponential stability of the self-similar profile in a quasi parabolic-elliptic regim…
On the Krein-Rutman theorem and beyond
Claudia Fonte Sanchez, Pierre Gabriel, Stéphane Mischler
In this work, we revisit the Krein-Rutman theory for semigroups of positive operators in a Banach lattice framework and we provide some very general, efficient and handy results wi…
Harris-type results on geometric and subgeometric convergence to equilibrium for stochastic semigroups
José A. Cañizo, Stéphane Mischler
We provide simple and constructive proofs of Harris-type theorems on the existence and uniqueness of an equilibrium and the speed of equilibration of discrete-time and continuous-t…
Special macroscopic modes and hypocoercivity
Kleber Carrapatoso, Jean Dolbeault, Frédéric Hérau +3
We study linear inhomogeneous kinetic equations with an external confining potential and a collision operator admitting several local conservation laws (local density, momentum and…
Hypocoercivity for kinetic linear equations in bounded domains with general Maxwell boundary condition
Armand Bernou, Kleber Carrapatoso, Stéphane Mischler +1
We establish the convergence to the equilibrium for various linear collisional kinetic equations (including linearized Boltzmann and Landau equations) with physical local conservat…
Weighted Korn and Poincaré-Korn inequalities in the Euclidean space and associated operators
Kleber Carrapatoso, Jean Dolbeault, Frédéric Hérau +2
We prove functional inequalities on vector fields on the Euclidean space when it is equipped with a bounded measure that satisfies a Poincaré inequality, and study associated self-…
Hypocoercivity without confinement
Emeric Bouin, Jean Dolbeault, Stéphane Mischler +2
In this paper, hypocoercivity methods are applied to linear kinetic equations with mass conservation and without confinement, in order to prove that the solutions have an algebraic…
Landau equation for very soft and Coulomb potentials near Maxwellians
Kleber Carrapatoso, Stéphane Mischler
This work deals with the Landau equation for very soft and Coulomb potentials near the associated Maxwellian equilibrium. We first investigate the corresponding linearized operator…
Towards an -theorem for granular gases
M. I. García de Soria, P. Maynar, S. Mischler +3
The -theorem, originally derived at the level of Boltzmann non-linear kinetic equation for a dilute gas undergoing elastic collisions, strongly constrains the velocity distribut…
Relaxation in time elapsed neuron network models in the weak connectivity regime
S Mischler, Q Weng
In order to describe the firing activity of a homogenous assembly of neurons, we consider time elapsed models, which give mathematical descriptions of the probability density of ne…
Uniqueness and long time asymptotics for the parabolic-parabolic Keller-Segel equation
Kleber Carrapatoso, Stéphane Mischler
The present paper deals with the parabolic-parabolic Keller-Segel equation in the plane inthe general framework of weak (or "free energy") solutions associated to an initial datum…
Kac's chaos and Kac's program
Stéphane Mischler
In this note I present the main results about the quantitative and qualitative propagation of chaos for the Boltzmann-Kac system obtained in collaboration with C. Mouhot in \cite{M…
Spectral analysis of semigroups and growth-fragmentation equations
Stéphane Mischler, Justine Scher
The aim of this paper is twofold: (1) On the one hand, the paper revisits the spectral analysis of semigroups in a general Banach space setting. It presents some new and more gener…
Uniqueness and long time asymptotic for the Keller-Segel equation: The parabolic-elliptic case
Fernandez Giani Egana, Stéphane Mischler
The present paper deals with the parabolic-elliptic Keller-Segel equation in the plane in the general framework of weak (or ''free energy") solutions associated to initial datum wi…
Rate of convergence of the Nanbu particle system for hard potentials
Nicolas Fournier, Stéphane Mischler
We consider the (numerically motivated) Nanbu stochastic particle system associated to the spatially homogeneous Boltzmann equation for true hard potentials. We establish a rate of…
Propagation of chaos for the 2D viscous vortex model
Nicolas Fournier, Maxime Hauray, Stéphane Mischler
We consider a stochastic system of particles, usually called vortices in that setting, approximating the 2D Navier-Stokes equation written in vorticity. Assuming that the initi…
On Kac's Chaos And Related Problems
Maxime Hauray, Stéphane Mischler
This paper is devoted to establish quantitative and qualitative estimates related to the notion of chaos as firstly formulated by M. Kac in his study of mean-field limit for system…
Kac's Program in Kinetic Theory
Stéphane Mischler, Clément Mouhot
This paper is devoted to the study of propagation of chaos and mean-field limits for systems of indistinguable particles, undergoing collision processes. The prime examples we will…
Rate of convergence to self-similarity for the fragmentation equation in L^1 spaces
María J. Cáceres, José A. Cañizo, Stéphane Mischler
In a recent result by the authors (ref. [1]) it was proved that solutions of the self-similar fragmentation equation converge to equilibrium exponentially fast. This was done by sh…
A new approach to quantitative propagation of chaos for drift, diffusion and jump processes
Stéphane Mischler, Clément Mouhot, Bernt Wennberg
This paper is devoted the the study of the mean field limit for many-particle systems undergoing jump, drift or diffusion processes, as well as combinations of them. The main resul…
Rate of convergence to an asymptotic profile for the self-similar fragmentation and growth-fragmentation equations
María J. Cáceres, José A. Cañizo, Stéphane Mischler
We study the asymptotic behavior of linear evolution equations of the type \partial_t g = Dg + Lg - λg, where L is the fragmentation operator, D is a differential operator, and λ i…