The Schauder estimate in kinetic theory with application to a toy nonlinear model
Analysis of PDEs
2020-07-22 v3
Abstract
This article is concerned with the Schauder estimate for linear kinetic Fokker-Planck equations with H\"older continuous coefficients. This equation has an hypoelliptic structure. As an application of this Schauder estimate, we prove the global well-posedness of a toy nonlinear model in kinetic theory. This nonlinear model consists in a non-linear kinetic Fokker-Planck equation whose steady states are Maxwellian and whose diffusion in the velocity variable is proportional to the mass of the solution.
Keywords
Cite
@article{arxiv.1801.07891,
title = {The Schauder estimate in kinetic theory with application to a toy nonlinear model},
author = {Cyril Imbert and Clément Mouhot},
journal= {arXiv preprint arXiv:1801.07891},
year = {2020}
}