Existence and continuous dependence of large solutions for the magnetohydrodynamic equations
Existence and continuous dependence of large solutions for the magnetohydrodynamic equations
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DOI：
10.1007/s00033-003-1017-z
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发表时间：
2003-07-01
影响因子：
2
通讯作者：
Wang, DH
中科院分区：
文献类型：
--
作者：
Chen, GQ;Wang, DH
研究了具有一般大初值的非线性磁流体动力学（MHD）方程的整体解。首先，在H-1中，在大初值条件下，证明了整体解的存在唯一性。结果表明，无论是冲击波，也没有真空和浓度在有限的时间内开发，虽然有一个复杂的流体动力学和磁动力学效应之间的相互作用。然后证明了解对初值的连续依赖性。并证明了系统在欧拉坐标系和拉格朗日坐标系下的适定性问题的等价性。
Global solutions of the nonlinear magnetohydrodynamic (MHD) equations with general large initial data are investigated. First the existence and uniqueness of global solutions are established with large initial data in H-1. It is shown that neither shock waves nor vacuum and concentration are developed in a finite time, although there is a complex interaction between the hydrodynamic and magnetodynamic effects. Then the continuous dependence of solutions upon the initial data is proved. The equivalence between the well-posedness problems of the system in Euler and Lagrangian coordinates is also showed.