Local well-posedness for a class of singular Vlasov equations

Thomas Chaub

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arXiv · 2202.07287

Local well-posedness for a class of singular Vlasov equations

Thomas Chaub

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Abstract

In this article we study a singular Vlasov system on the torus where the force field has the smoothness of a (fractional) derivative $D^{\alpha}$ of the density, where $\alpha>0$. We prove local well-posedness in Sobolev spaces without restriction on the data. This is in sharp contrast with the case $\alpha=0$ which is ill-posed in Sobolev spaces for general data.

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Thomas Chaub. 2022-02-15. Local well-posedness for a class of singular Vlasov equations. https://arxiv.org/abs/2202.07287

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