Existence of Local Solutions to a Free Boundary Problem for Incompressible Viscous Magnetohydrodynamics

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-07-04 DOI:10.1007/s00021-024-00879-y

Piotr Kacprzyk, Wojciech M. Zaja̧czkowski

引用次数: 0

Abstract

We consider the motion of an incompressible magnetohydrodynamics with resistivity in a domain bounded by a free surface which is coupled through the free surface with an electromagnetic field generated by a magnetic field prescribed on an exterior fixed boundary. On the free surface, transmission conditions for the electromagnetic field are imposed. As transmission condition we assume jumps of tangent components of magnetic and electric fields on the free surface. We prove local existence of solutions such that velocity and magnetic fields belong to \(H^{2+\alpha ,1+\alpha /2}\), \(\alpha >5/8\).

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不可压缩粘性磁流体力学自由边界问题局部解的存在性

我们考虑了不可压缩磁流体力学在自由表面所限定的域中的运动，该域通过自由表面与外部固定边界上规定的磁场所产生的电磁场耦合。在自由表面上，施加了电磁场的传输条件。作为传输条件，我们假设磁场和电场的切线分量在自由表面上跳跃。我们证明了解的局部存在性，即速度场和磁场属于（H^{2+\alpha ,1+\alpha /2}\）、（\alpha >5/8\）。

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.