On an initial boundary value problem for the equations of ideal magneto-hydrodynamics

We study an initial boundary value problem for the symmetric hyperbolic quasilinear system of the equations of ideal magneto-hydrodynamics with a perfectly conducting wall boundary condition. Existence of a unique classical solution is proved inside a suitable class of functions of Sobolev type. Moreover, solutions inside the above class are shown to depend continuously in strong norm on the data.