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arXiv · 1908.02636

Global well-posedness of magnetohydrodynamic equations

Chengfei Ai·Zhong Tan·Jianfeng Zhou
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Abstract

We study the global well-posedness of magnetohydrodynamic (MHD) equations. The hydrodynamic system consists of the Navier-Stokes equations for the fluid velocity coupled with a reduced from of the Maxwell equations for the magnetic field. The fluid velocity is assumed to satisfy a no-slip boundary condition, while the magnetic field is subject to a time-dependent Dirichlet boundary condition. We first establish the global existence of weak and strong solutions to (1.1)-(1.4). Then we derive the existence of a uniform attractor for (1.1)-(1.4).

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Chengfei Ai, Zhong Tan, Jianfeng Zhou. 2019-08-07. Global well-posedness of magnetohydrodynamic equations. https://arxiv.org/abs/1908.02636

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