Existence and continuous dependence of large solutions forthe magnetohydrodynamic equations

Global solutions of the nonlinear magnetohydrodynamic (MHD) equations with general large initial data are investigated. First the existence and uniqueness of global solutions areestablished with large initial data in H ¹. It is shown that neither shock waves nor vacuum andconcentration are developed in a finite time, although there is a complex interaction between thehydrodynamic and magnetodynamic effects. Then the continuous dependence of solutions uponthe initial data is proved. The equivalence between the well-posedness problems of the systemin Euler and Lagrangian coordinates is also showed.