2018/01/24 by Imbert, Cyril, Mouhot, Clément
#Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.1801.07891
This article is concerned with the Schauder estimate for linear kinetic Fokker-Planck equations with Hölder 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.