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Pré-Publication, Document De Travail Année : 2018

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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Dates et versions

hal-01690354 , version 1 (23-01-2018)
hal-01690354 , version 2 (23-07-2019)
hal-01690354 , version 3 (14-07-2020)

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Cyril Imbert, Clément Mouhot. A toy nonlinear model in kinetic theory. 2018. ⟨hal-01690354v1⟩
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