The Schauder estimate in kinetic theory with application to a toy nonlinear model

Cyril Imbert (1) , Clément Mouhot (2)

1 DMA - Département de Mathématiques et Applications - ENS Paris
2 DPMMS - Department of Pure Mathematics and Mathematical Statistics

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.

Domaines: Equations aux dérivées partielles [math.AP]

Cyril Imbert, Clément Mouhot. The Schauder estimate in kinetic theory with application to a toy nonlinear model. Annales Henri Lebesgue, 2021, 4, pp.369-405. ⟨10.5802/ahl.75⟩. ⟨hal-01690354v3⟩