一类奇异Vlasov方程的局部适定性

IF 1 4区数学 Q1 MATHEMATICS

Kinetic and Related Models Pub Date : 2022-02-15 DOI:10.3934/krm.2022027

Thomas Chaub

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引用次数: 0

摘要

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

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Local well-posedness for a class of singular Vlasov equations

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来源期刊

Kinetic and Related Models 数学-数学

CiteScore

2.10

自引率

10.00%

发文量

审稿时长

>12 weeks

期刊介绍： KRM publishes high quality papers of original research in the areas of kinetic equations spanning from mathematical theory to numerical analysis, simulations and modelling. It includes studies on models arising from physics, engineering, finance, biology, human and social sciences, together with their related fields such as fluid models, interacting particle systems and quantum systems. A more detailed indication of its scope is given by the subject interests of the members of the Board of Editors. Invited expository articles are also published from time to time.