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arXiv · 2205.12930

Kinetic Schauder estimates with time-irregular coefficients and uniqueness for the Landau equation

Christopher Henderson·Weinan Wang
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Abstract

We prove a Schauder estimate for kinetic Fokker-Planck equations that requires only H\"older regularity in space and velocity but not in time. As an application, we deduce a weak-strong uniqueness result of classical solutions to the spatially inhomogeneous Landau equation beginning from initial data having H\"older regularity in $x$ and only a logarithmic modulus of continuity in $v$. This replaces an earlier result requiring H\"older continuity in both variables.

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Christopher Henderson, Weinan Wang. 2022-05-25. Kinetic Schauder estimates with time-irregular coefficients and uniqueness for the Landau equation. https://arxiv.org/abs/2205.12930

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