Global well-posedness of magnetohydrodynamic equations

2019/08/07 by Chengfei Ai, Ai, Chengfei, Zhong Tan +3
Engineering · Mathematics · #35B65 #35Q35 #76N10 #76W05 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1908.02636

openalex publication_date 2019/08/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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).

Citations

• Sur le mouvement d'un liquide visqueux emplissant l'espace
• Nonlinear Schrödinger evolution equations

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