The Schauder estimate in kinetic theory with application to a toy nonlinear model
Annales Henri Lebesgue, Volume 4 (2021) , pp. 369-405.

Metadata

KeywordsFokker–Planck equation, hypoelliptic, Schauder estimate, nonlinear kinetic equation

Abstract

This article is concerned with the Schauder estimate for linear kinetic Fokker–Planck equations with Höder 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.


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