97 citations · 119 across the 17 of their papers we have counts for
17 papers
Velocity Averaging Lemmas: Classical, Quantum and Semi-Classical
François Golse, Norbert J. Mauser, Jakob Möller
Averaging lemmas were introduced as a tool of the mathematical analysis of kinetic equations, i.e. PDEs for functions in phase space containing a transport ("advection") te…
Velocity Averaging for the Wigner Kinetic Equation in the Semiclassical Regime
François Golse, Jakob Möller
This paper discusses the possibility of applying the velocity averaging theorems in [F. Golse, P.-L. Lions, B. Perthame, R. Sentis: J. Funct. Anal. 76(1):110--125, 1988] to the Wig…
Local Conservation Laws and Entropy Inequality for Kinetic Models with Delocalized Collision Integrals
Frédérique Charles, Zhe Chen, François Golse
This article presents a common setting for the collision integrals appearing in the kinetic theory of dense gases. It includes the collision integrals of the Enskog e…
Partial regularity in time for the space-homogeneous Boltzmann equation with very soft potentials
François Golse, Cyril Imbert, Luis Silvestre
We prove that the set of singular times for weak solutions of the homogeneous Boltzmann equation with very soft potentials constructed as in Villani (1998) has Hausdorff dimension…
Validité de la théorie cinétique des gaz: au-delà de l'équation de Boltzmann [d'après T. Bodineau, I. Gallagher, L. Saint-Raymond, S. Simonella]
François Golse
Obtaining a rigorous justification of the kinetic theory of gases from Newton's second law of dynamics for a large number of identical spheres interacting by elastic binary collisi…
Quantum Optimal Transport: Quantum Couplings and Many-Body Problems
François Golse
This text is a set of lecture notes for a 4.5-hour course given at the Erdös Center (Rényi Institute, Budapest) during the Summer School "Optimal Transport on Quantum Structures" (…
Local regularity for the space-homogeneous Landau equation with very soft potentials
François Golse, Cyril Imbert, Sehyun Ji +1
This paper deals with the space-homogenous Landau equation with very soft potentials, including the Coulomb case. This nonlinear equation is of parabolic type with diffusion matrix…
Mean-Field Limits in Statistical Dynamics
François Golse
These lectures notes are aimed at introducing the reader to some recent mathematical tools and results for the mean-field limit in statistical dynamics. As a warm-up, lecture 1 rev…
Time Dependent Quantum Perturbations Uniform in the Semiclassical Regime
François Golse, Thierry Paul
We present a time dependent quantum perturbation result, uniform in the Planck constant, for perturbations of potentials whose gradients are Lipschitz continuous by potentials whos…
Quantum and Semiquantum Pseudometrics and Applications
François Golse, Thierry Paul
We establish a Kantorovich duality for the pseudometric introduced in [F. Golse, T. Paul, Arch. Rational Mech. Anal. 223 (2017), 57--94], obtained from the usua…
Observability for the Schrödinger Equation: an Optimal Transport Approach
François Golse, Thierry Paul
We establish an observation inequality for the Schrödinger equation on , uniform in the Planck constant . The proof is based on the pseudometric introd…
Towards Optimal Transport for Quantum Densities
Emanuele Caglioti, François Golse, Thierry Paul
An analogue of the quadratic Wasserstein (or Monge-Kantorovich) distance between Borel probability measures on has been defined in [F. Golse, C. Mouhot, T. Paul: Com…
Semiclassical Evolution With Low Regularity
François Golse, Thierry Paul
We prove semiclassical estimates for the Schr\''odinger-von Neumann evolution with potentials and density matrices whose square root have either Wigner functions with low…
The Random Batch Method for -Body Quantum Dynamics
François Golse, Shi Jin, Thierry Paul
This paper discusses a numerical method for computing the evolution of large interacting system of quantum particles. The idea of the random batch method is to replace the total in…
Partial Regularity in Time for the Space Homogeneous Landau Equation with Coulomb Potential
François Golse, Maria Pia Gualdani, Cyril Imbert +1
We prove that the set of singular times for weak solutions of the space homogeneous Landau equation with Coulomb potential constructed as in [C. Villani, Arch. Rational Mech. Anal.…
Hölder regularity for hypoelliptic kinetic equations with rough diffusion coefficients
François Golse, Alexis Vasseur
This paper is dedicated to the application of the DeGiorgi-Nash-Moser regularity theory to the kinetic Fokker-Planck equation. This equation is hypoelliptic. It is parabolic only i…
The Incompressible Navier-Stokes Limit of the Boltzmann Equation for Hard Cutoff Potentials
François Golse, Laure Saint-Raymond
The present paper proves that all limit points of sequences of renormalized solutions of the Boltzmann equation in the limit of small, asymptotically equivalent Mach and Knudsen nu…