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

IF 1.2 3区数学 Q2 MATHEMATICS, APPLIED

Journal of Mathematical Fluid Mechanics 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

Journal of Mathematical Fluid Mechanics 物理-力学

CiteScore

2.00

自引率

15.40%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Mathematical Fluid Mechanics (JMFM)is a forum for the publication of high-quality peer-reviewed papers on the mathematical theory of fluid mechanics, with special regards to the Navier-Stokes equations. As an important part of that, the journal encourages papers dealing with mathematical aspects of computational theory, as well as with applications in science and engineering. The journal also publishes in related areas of mathematics that have a direct bearing on the mathematical theory of fluid mechanics. All papers will be characterized by originality and mathematical rigor. For a paper to be accepted, it is not enough that it contains original results. In fact, results should be highly relevant to the mathematical theory of fluid mechanics, and meet a wide readership.