Local well-posedness for a class of singular Vlasov equations

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-02-15 DOI:10.3934/krm.2022027

Thomas Chaub

引用次数: 0

Abstract

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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一类奇异Vlasov方程的局部适定性

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.