Uniform Regularity for Incompressible MHD Equations in a Bounded Domain with Curved Boundary in 3D

2024/04/17 by Yingzhi Du, Tao Luo, Du, Yingzhi +1
Engineering · Mathematics · #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2404.11197

openalex publication_date 2024/04/17 · openalex created_date 2024/04/19 · openalex updated_date 2026/07/28

Abstract

For the initial boundary problem of the incompressible MHD equations in a bounded domain with general curved boundary in 3D with the general Navier-slip boundary conditions for the velocity field and the perfect conducting condition for the magnetic field, we establish the uniform regularity of conormal Sobolev norms and Lipschitz norms to addressing the anisotropic regularity of tangential and normal directions, which enable us to prove the vanishing dissipation limit as the viscosity and the magnetic diffusion coefficients tend to zero. We overcome the difficulties caused by the intricate interaction of boundary curvature, velocity field, and magnetic fields and resolve the issue caused by the problem that the viscosity and the magnetic diffusion coefficients are not required to be equal.

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