Uniqueness and regularity of weak solutions of a fluid-rigid body interaction system under the Prodi-Serrin condition

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-01-01 DOI:10.3934/dcds.2023123

Debayan Maity, Takéo Takahashi

引用次数: 1

Abstract

In this article, we study the weak uniqueness and the regularity of the weak solutions of a fluid-structure interaction system. More precisely, we consider the motion of a rigid ball in a viscous incompressible fluid and we assume that the fluid-rigid body system fills the entire space $ \mathbb{R}^{3}. $ We prove that the corresponding weak solutions that additionally satisfy a classical Prodi-Serrin condition, including a critical one, are unique. We also show that the weak solutions are regular under the Prodi-Serrin conditions, with a smallness condition in the critical case.

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Prodi-Serrin条件下流体-刚体相互作用系统弱解的唯一性和规律性

本文研究了流固耦合系统弱解的弱唯一性和正则性。更准确地说，我们考虑一个刚体球在粘性不可压缩流体中的运动，我们假设流体-刚体系统填满整个空间$ \mathbb{R}^{3}。证明了附加满足经典Prodi-Serrin条件的弱解是唯一的，其中包括一个临界解。我们还证明了弱解在Prodi-Serrin条件下是正则解，在临界情况下是小解。

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.