可压缩MHD系统的物理接地边界条件

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations Pub Date : 2025-10-10 DOI:10.1016/j.jde.2025.113802

Jan Březina , Eduard Feireisl

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引用次数: 0

摘要

我们考虑一个一般的可压缩MHD系统，其中磁场在非均质介质中传播。使用适当的输运系数惩罚，我们执行了几个奇异极限。结果我们得到：1。有界域上可压缩MHD系统物理接地边界条件的严格证明在流体域外麦克斯韦感应方程成立的情况下，任意有限能量初始数据弱解的存在性。为几何边界复杂域的数值实验提供了一个合适的理论平台。

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On physically grounded boundary conditions for the compressible MHD system

We consider a general compressible MHD system, where the magnetic field propagates in a heterogeneous medium. Using suitable penalization in terms of the transport coefficients we perform several singular limits. As a result we obtain:

1.
A rigorous justification of physically grounded boundary conditions for the compressible MHD system on a bounded domain.
2.
Existence of weak solutions for arbitrary finite energy initial data in the situation the Maxwell induction equation holds also outside the fluid domain.
3.
A suitable theoretical platform for numerical experiments on domains with geometrically complicated boundaries.

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来源期刊

Journal of Differential Equations 数学-数学

CiteScore

4.40

自引率

8.30%

发文量

543

审稿时长

9 months

期刊介绍： The Journal of Differential Equations is concerned with the theory and the application of differential equations. The articles published are addressed not only to mathematicians but also to those engineers, physicists, and other scientists for whom differential equations are valuable research tools. Research Areas Include: • Mathematical control theory • Ordinary differential equations • Partial differential equations • Stochastic differential equations • Topological dynamics • Related topics