A toy nonlinear model in kinetic theory
Résumé
This note is concerned with the study of a toy nonlinear model in kinetic theory. It consists in a non-linear kinetic Fokker-Planck equation whose diffusion in the velocity variable is proportional to the mass of the solution and steady states are Maxwellian. Solutions are constructed by combining energy estimates, well-designed hypoelliptic Schauder estimates, and the hypoelliptic extension of the De Giorgi-Nash Hölder estimates obtained recently by Golse, Vasseur and the two authors (2017).
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