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Volume 3, Issue 2
The Incompressible Limit of the Equations of Compressible Ideal Magneto-Hydrodynamics with Perfectly Conducting Boundary

Paolo Secchi

DOI: 10.4208/cmaa.2024-0009

Commun. Math. Anal. Appl., 3 (2024), pp. 168-198.

Published online: 2024-07

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  • Abstract

We consider the initial-boundary value problem in the halfspace for the system of equations of ideal magneto-hydrodynamics (MHD) 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.

  • Keywords

Compressible ideal magneto-hydrodynamics, Mach number, incompressible limit, singular limit, perfectly conducting wall.

  • AMS Subject Headings

35L50, 35Q35, 76M45, 76W05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMAA-3-168, author = {Secchi , Paolo}, title = {The Incompressible Limit of the Equations of Compressible Ideal Magneto-Hydrodynamics with Perfectly Conducting Boundary}, journal = {Communications in Mathematical Analysis and Applications}, year = {2024}, volume = {3}, number = {2}, pages = {168--198}, abstract = {

We consider the initial-boundary value problem in the halfspace for the system of equations of ideal magneto-hydrodynamics (MHD) 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.

}, issn = {2790-1939}, doi = {https://doi.org/10.4208/cmaa.2024-0009}, url = {http://global-sci.org/intro/article_detail/cmaa/23227.html} }
TY - JOUR T1 - The Incompressible Limit of the Equations of Compressible Ideal Magneto-Hydrodynamics with Perfectly Conducting Boundary AU - Secchi , Paolo JO - Communications in Mathematical Analysis and Applications VL - 2 SP - 168 EP - 198 PY - 2024 DA - 2024/07 SN - 3 DO - http://doi.org/10.4208/cmaa.2024-0009 UR - https://global-sci.org/intro/article_detail/cmaa/23227.html KW - Compressible ideal magneto-hydrodynamics, Mach number, incompressible limit, singular limit, perfectly conducting wall. AB -

We consider the initial-boundary value problem in the halfspace for the system of equations of ideal magneto-hydrodynamics (MHD) 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.

Paolo Secchi. (2024). The Incompressible Limit of the Equations of Compressible Ideal Magneto-Hydrodynamics with Perfectly Conducting Boundary. Communications in Mathematical Analysis and Applications. 3 (2). 168-198. doi:10.4208/cmaa.2024-0009
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