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arXiv · 1801.07891

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

Cyril Imbert·Clément Mouhot
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Abstract

This article is concerned with the Schauder estimate for linear kinetic Fokker-Planck equations with H\"older 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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Cyril Imbert, Clément Mouhot. 2018-01-24. The Schauder estimate in kinetic theory with application to a toy nonlinear model. https://arxiv.org/abs/1801.07891

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