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 - <p style="text-align: justify;">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.</p>