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arXiv · 2407.08785

A kinetic Nash inequality and precise boundary behavior of the kinetic Fokker-Planck equation

Christopher Henderson·Giacomo Lucertini·Weinan Wang
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Abstract

In this paper, we prove a kinetic Nash type inequality and adapt it to a new functional inequality for functions in a kinetic Sobolev space with absorbing boundary conditions on the half-space. As an application, we address the boundary behavior of the kinetic Fokker-Planck equations in the half-space. Our main result is the sharp regularity of the solution at the absorbing boundary and grazing set.

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Christopher Henderson, Giacomo Lucertini, Weinan Wang. 2024-07-11. A kinetic Nash inequality and precise boundary behavior of the kinetic Fokker-Planck equation. https://arxiv.org/abs/2407.08785

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