Uniform Regularity for Incompressible MHD Equations in a Bounded Domain with Curved Boundary in 3D
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914758204063744 |
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| author | Du, Yingzhi Luo, Tao |
| author_facet | Du, Yingzhi Luo, Tao |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_11197 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Uniform Regularity for Incompressible MHD Equations in a Bounded Domain with Curved Boundary in 3D Du, Yingzhi Luo, Tao Analysis of PDEs 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. |
| title | Uniform Regularity for Incompressible MHD Equations in a Bounded Domain with Curved Boundary in 3D |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2404.11197 |