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...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.展开更多
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)
文摘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.
