The Incompressible Limit of the Equations of Compressible Ideal Magneto-Hydrodynamics with perfectly conducting boundary
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916310200352768 |
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| author | Secchi, Paolo |
| author_facet | Secchi, Paolo |
| contents | We consider the initial-boundary value problem in the halfspace for the system of equations of ideal Magneto-Hydrodynamics with a perfectly conducting wall boundary condition. We show the convergence of solutions to the solution of the equations of incompressible MHD as the Mach number goes to zero. Because of the characteristic boundary, where a loss of regularity in the normal direction to the boundary may occur, the convergence is shown in suitable anisotropic Sobolev spaces which take account of the singular behavior at the boundary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_11425 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Incompressible Limit of the Equations of Compressible Ideal Magneto-Hydrodynamics with perfectly conducting boundary Secchi, Paolo Analysis of PDEs 35L50 (Primary) 35Q35, 76M45, 76W05 (Secondary) We consider the initial-boundary value problem in the halfspace for the system of equations of ideal Magneto-Hydrodynamics with a perfectly conducting wall boundary condition. We show the convergence of solutions to the solution of the equations of incompressible MHD as the Mach number goes to zero. Because of the characteristic boundary, where a loss of regularity in the normal direction to the boundary may occur, the convergence is shown in suitable anisotropic Sobolev spaces which take account of the singular behavior at the boundary. |
| title | The Incompressible Limit of the Equations of Compressible Ideal Magneto-Hydrodynamics with perfectly conducting boundary |
| topic | Analysis of PDEs 35L50 (Primary) 35Q35, 76M45, 76W05 (Secondary) |
| url | https://arxiv.org/abs/2406.11425 |