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| The Zero Mach Number Limit of the Three-Dimensional CompressibleViscous Magnetohydrodynamic Equations |
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Citation： |
Yeping LI,Wen'an YONG.The Zero Mach Number Limit of the Three-Dimensional CompressibleViscous Magnetohydrodynamic Equations[J].Chinese Annals of Mathematics B,2015,36(6):1043~1054 |
| Page view： 1302
Net amount： 1023 |
Authors： |
Yeping LI; Wen'an YONG |
Foundation： |
This work was supported by the National Natural Science
Foundation of China (No.\,11171223), the Doctoral Program Foundation
of Ministry of Education of China (No.\,20133127110007) and the
Innovation Program of Shanghai Municipal Education Commission
(No.\,13ZZ109). |
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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. |
Keywords： |
Compressible viscous MHD equation, Mach number limit,
Convergence-stability principle, Incompressible viscous MHD
equation, Energy-type error estimate
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Classification： |
76W05, 35B40 |
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