文献类型：期刊文献

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

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

作者：Yeping LI[1];Wen'an YONG[2]

机构：[1]Department of Mathematics, East China University of Science and Technology;[2]Zhou Pei-Yuan Center for Applied Mathematics, Tsinghua University

年份：2015

卷号：36

期号：6

起止页码：1043

中文期刊名：Chinese Annals of Mathematics,Series B

外文期刊名：数学年刊（B辑英文版）

收录：CSTPCD;;Scopus;CSCD:【CSCD2015_2016】；

基金：supported by the National Natural Science Foundation of China(No.11171223);the Doctoral Program Foundation of Ministry of Education of China(No.20133127110007);the Innovation Program of Shanghai Municipal Education Commission(No.13ZZ109)

语种：英文

中文关键词：Compressible viscous MHD equation; Mach number limit; Convergence-stability principle; Incompressible viscous MHD equation; Energy-typeerror estimate

外文关键词：流体动力学方程;三维可压缩;马赫数;粘性;全局光滑解;周期初值问题;不可压缩;收敛速度

摘要：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 equa- tions, first the convergence-stability principle is established. Then it is shown that, when the Much 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 mag- netohydrodynamic 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 Much number goes to zero. Moreover, the authors prove the convergence of smooth solutions of the equa- tions towards those of the incompressible viscous magnetohydrodynamic equations with a sharp convergence rate.