Low Mach number limit of the full compressible mhd equations with Cattaneo’s heat transfer law

We study low Mach number limit of the full compressible magnetohydrodynamic (MHD) equations with Cattaneo’s heat transfer law in the framework of classical solutions with small density, temperature and heat flux variations. It is rigorously justified that, for well-prepared initial data and a sufficiently small Mach number, the full compressible MHD equations with Cattaneo’s heat transfer law admit a smooth solution on the time interval where the smooth solution of the incompressible MHD equations exists, and the solution of the former converges to that of the latter as the Mach number tends to zero. Moreover, we also obtain the convergence rate.

Keywords

full compressible MHD equations, Cattaneo’s heat transfer law, low Mach number limit, incompressible MHD equations

2010 Mathematics Subject Classification

35B40, 76W05

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This work is supported by NSFC (Grant Nos. 12071212, 11971234), a project funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions, and the program B for Outstanding PhD candidate of Nanjing University.

Received 12 March 2021

Received revised 5 January 2022

Accepted 7 January 2022

Published 26 May 2022