The zero Mach number limit of the three-dimensional compressible viscous magnetohydrodynamic equations
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This paper is concerned with the zeroMach number limit of the three-dimensional compressible viscous magnetohydrodynamic equations. More precisely, based on the local existence of the three-dimensional compressible viscous magnetohydrodynamic equations, first the convergence-stability principle is established. Then it is shown that, when the Mach number is sufficiently small, the periodic initial value problems of the equations have a unique smooth solution in the time interval, where the incompressible viscous magnetohydrodynamic equations have a smooth solution. When the latter has a global smooth solution, the maximal existence time for the former tends to infinity as the Mach number goes to zero. Moreover, the authors prove the convergence of smooth solutions of the equations towards those of the incompressible viscous magnetohydrodynamic equations with a sharp convergence rate.
KeywordsCompressible viscous MHD equation Mach number limit Convergence-stability principle Incompressible viscous MHD equation Energy-type error estimate
2000 MR Subject Classification76W05 35B40
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