The Incompressible Limit of the Equations of Compressible Ideal Magneto-Hydrodynamics with Perfectly Conducting Boundary
Year: 2024
Author: Paolo Secchi
Communications in Mathematical Analysis and Applications, Vol. 3 (2024), Iss. 2 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cmaa.2024-0009
Communications in Mathematical Analysis and Applications, Vol. 3 (2024), Iss. 2 : pp. 168–198
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 31
Keywords: Compressible ideal magneto-hydrodynamics Mach number incompressible limit singular limit perfectly conducting wall.