三维曲面边界有界区域不可压缩MHD方程的一致正则性

IF 2.3 2区 数学 Q1 MATHEMATICS Journal of Differential Equations Pub Date : 2025-02-25 Epub Date: 2024-11-29 DOI:10.1016/j.jde.2024.11.028
Yingzhi Du, Tao Luo
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引用次数: 0

摘要

对于三维一般曲面边界有界区域内不可压缩MHD方程的初始边界问题,在速度场的一般Navier-slip边界条件和磁场的完美导通条件下,建立了共法Sobolev范数和Lipschitz范数的均匀正则性,解决了切向和法向的各向异性正则性问题。从而证明了黏度和磁扩散系数趋于零时的消散极限。克服了边界曲率、速度场和磁场复杂相互作用所带来的困难,解决了黏度和磁扩散系数不相等的问题。
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Uniform regularity for incompressible MHD equations in a bounded domain with curved boundary in 3D
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 equal.
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来源期刊
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
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