关于 R3 中静止 MHD 的柳维尔类型结果

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED

Nonlinearity Pub Date : 2024-07-17 DOI:10.1088/1361-6544/ad6128

Dongho Chae and Jihoon Lee

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引用次数: 0

摘要

本文关注稳定不可压缩磁流体动力学（MHD）方程的柳维尔类型定理。我们确定，在 (v, b) 的可整性假设条件下，稳定 MHD 方程的解是等效零。我们特别指出，流体速度的强可整性条件和磁场的弱可整性条件的组合给出了刘维尔类型定理的充分条件。此外，我们还证明，流体速度势的增长条件与磁场的可整性条件相结合，会导致解的三重性。

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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On Liouville type results for the stationary MHD in R3

This paper is concerned with the Liouville type theorems for the steady incompressible magnetohydrodynamics (MHD) equations. We establish that the solution to the steady MHD equations is identically zero under the integrability assumptions on (v, b). We show that, in particular, a combination of a strong integrability condition on the velocity of a fluid and a weak integrability condition on the magnetic field gives a sufficient condition on the Liouville type theorems. Furthermore, we show that the combination of the growth condition of the potential for the fluid velocity and the integrability condition for the magnetic field leads to the triviality of the solution.

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来源期刊

Nonlinearity 物理-物理：数学物理

CiteScore

3.00

自引率

5.90%

发文量

170

审稿时长

12 months

期刊介绍： Aimed primarily at mathematicians and physicists interested in research on nonlinear phenomena, the journal''s coverage ranges from proofs of important theorems to papers presenting ideas, conjectures and numerical or physical experiments of significant physical and mathematical interest. Subject coverage: The journal publishes papers on nonlinear mathematics, mathematical physics, experimental physics, theoretical physics and other areas in the sciences where nonlinear phenomena are of fundamental importance. A more detailed indication is given by the subject interests of the Editorial Board members, which are listed in every issue of the journal. Due to the broad scope of Nonlinearity, and in order to make all papers published in the journal accessible to its wide readership, authors are required to provide sufficient introductory material in their paper. This material should contain enough detail and background information to place their research into context and to make it understandable to scientists working on nonlinear phenomena. Nonlinearity is a journal of the Institute of Physics and the London Mathematical Society.