The purpose of this paper is to study the three-dimensional system of magnetohydrodynamic (MHD equations) for a viscous incompressible resistive fluid. We are interested in the existence of suitable weak solutions to the system in time varying domains. To do this, we consider the approximate equations related to the MHD equations and we apply the Leray-Schauder fixed point theorem to the solutions of the equations over the moving boundary domains. Existence of suitable weak solutions is established by the energy estimates and the compactness results in Lebesgue and Sobolev spaces.

中文翻译：

---

时变域中不可压缩磁流体动力学方程的弱解

本文的目的是研究粘性不可压缩电阻性流体的磁流体动力学三维系统（MHD方程）。我们对时变域中系统的合适弱解的存在感兴趣。为此，我们考虑了与MHD方程有关的近似方程，并将Leray-Schauder不动点定理应用于运动边界域上方程的解。通过能量估计确定合适弱解的存在性，并得出Lebesgue和Sobolev空间的紧致性。