文献类型：期刊文献

英文题名：The Zero Mach Number Limit of the Three-Dimensional Compressible Viscous Magnetohydrodynamic Equations

作者：Li, Yeping[1];Yong, Wen'an[2]

机构：[1]E China Univ Sci & Technol, Dept Math, Shanghai 200237, Peoples R China;[2]Tsinghua Univ, Zhou Pei Yuan Ctr Appl Math, Beijing 100084, Peoples R China

年份：2015

卷号：36

期号：6

起止页码：1043

外文期刊名：CHINESE ANNALS OF MATHEMATICS SERIES B

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000368325700013)】；

基金：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).

语种：英文

外文关键词：Compressible viscous MHD equation; Mach number limit; Convergence-stability principle; Incompressible viscous MHD equation; Energy-type error estimate

摘要：This paper is concerned with the zero Mach 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.