An initial boundary value problem in ideal magneto-hydrodynamics (Q1871715)

The equations of magneto-hydrodynamics for the motion of an electrically conducting fluid are considered when the effects of viscosity and electrical resistivity are neglected. The equations are studied in the half-space \(x_1 >0\), with with a perfectly conducting boundary condition. The functional space setting is provided by anisotropic Sobolev spaces which take into account the fact that the boundary is characteristic. The local existence of the regular solution is proved. The results improve previous results concerning this boundary value problem. Particularly, the regularity restriction \(m\geq 8\) is reduced now to \(m\geq 6\), with \(m\) standing for the order of the maximal Sobolev derivative.