Well-posedness and singularity formation for Vlasov–Riesz system

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-01-31 DOI:10.3934/krm.2023030

Young-Pil Choi, In-Jee Jeong

引用次数: 4

Abstract

We investigate the Cauchy problem for the Vlasov--Riesz system, which is a Vlasov equation featuring an interaction potential generalizing previously studied cases, including the Coulomb $\Phi = (-\Delta)^{-1}\rho$, Manev $(-\Delta)^{-1} + (-\Delta)^{-\frac12}$, and pure Manev $(-\Delta)^{-\frac12}$ potentials. For the first time, we extend the local theory of classical solutions to potentials more singular than that for the Manev. Then, we obtain finite-time singularity formation for solutions with various attractive interaction potentials, extending the well-known blow-up result of Horst for attractive Vlasov--Poisson for $d\ge4$. Our local well-posedness and singularity formation results extend to cases when linear diffusion and damping in velocity are present.

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Vlasov-Riesz系统的适位性和奇点形成

我们研究了Vlasov—Riesz系统的Cauchy问题，这是一个Vlasov方程，其特征是相互作用势推广了先前研究的情况，包括库仑$\Phi = (-\Delta)^{-1}\rho$，马涅夫$(-\Delta)^{-1} + (-\Delta)^{-\frac12}$和纯马涅夫$(-\Delta)^{-\frac12}$势。我们首次将经典解的局部理论推广到比马尼夫方程更奇异的势。然后，我们得到了具有各种吸引相互作用势的解的有限时间奇点形成，推广了众所周知的关于$d\ge4$的吸引Vlasov—Poisson的Horst爆破结果。我们的局部适定性和奇点形成结果推广到存在线性扩散和速度阻尼的情况。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.