The Zero Mach Number Limit of the Three-Dimensional Compressible
Viscous Magnetohydrodynamic Equations |
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Authors: | Yeping LI and Wen'an YONG |
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Institution: | Department of Mathematics, East China University of Science
and Technology, Shanghai 200237, China. and Zhou Pei-Yuan Center for Applied
Mathematics, Tsinghua University, Beijing 100084, China. |
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Abstract: | This paper is concerned with the zero Mach number limit of the
three-dimension- al 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. |
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Keywords: | Compressible viscous MHD equation Mach number limit Convergence-stability principle Incompressible viscous MHD
equation Energy-type error estimate
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