Existence of weak solutions to the two-dimensional incompressible Euler equations in the presence of sources and sinks

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-03-25 DOI:10.57262/ade027-1112-683

M. Bravin, F. Sueur

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引用次数: 5

Abstract

A classical model for sources and sinks in a two-dimensional perfect incompressible fluid occupying a bounded domain dates back to Yudovich’s paper [44] in 1966. In this model, on the one hand, the normal component of the fluid velocity is prescribed on the boundary and is nonzero on an open subset of the boundary, corresponding either to sources (where the flow is incoming) or to sinks (where the flow is outgoing). On the other hand the vorticity of the fluid which is entering into the domain from the sources is prescribed. In this paper we investigate the existence of weak solutions to this system by relying on a priori bounds of the vorticity, which satisfies a transport equation associated with the fluid velocity vector field. Our results cover the case where the vorticity has a Lp integrability in space, with p in [1,+∞], and prove the existence of solutions obtained by compactness methods from viscous approximations. More precisely we prove the existence of solutions which satisfy the vorticity equation in the distributional sense in the case where p > 4 3 , in the renormalized sense in the case where p > 1, and in a symmetrized sense in the case where p = 1.

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存在源和汇的二维不可压缩Euler方程弱解的存在性

二维完美不可压缩流体的源汇的经典模型可以追溯到1966年Yudovich的论文[44]。在该模型中，一方面，流体速度的法向分量在边界上是规定的，并且在边界的一个开放子集上是非零的，对应于源(流体进入的地方)或汇(流体流出的地方)。另一方面，从源进入域的流体的涡度是规定的。本文利用涡度的先验界，研究了该系统弱解的存在性，它满足与流体速度矢量场相关的输运方程。我们的结果涵盖了涡度在空间上具有Lp可积性的情况，p在[1，+∞]中，并证明了由粘性近似用紧性方法得到的解的存在性。更确切地说，我们证明了在分布意义上满足涡度方程的解的存在性，在重正化意义上满足涡度方程的解，在重正化意义上满足涡度方程的解，在p = 1的情况下，在对称意义上满足涡度方程的解。

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.