The initial boundary value problem for the equations of ideal magneto- hydrodynamics
The author proves a local in time existence and uniqueness theorem for the initial boundary value problem of the equations of ideal magnetohydrodynamics over a bounded domain \(\Omega \subset R^ 3\) with \(C^{\infty}\) boundary \(\Gamma\). The initial pressure and magnetic field are chosen such that the equations form a quasilinear symmetric hyperbolic system. Defining appropriate function spaces, the theorem is proved via iteration scheme. At first, the equations are modified to make the boundary noncharacteristic. Secondly, making use of the special structure of the modified equations and the rank of the boundary matrix, it is shown that the limit of the solutions of the modified equations is the solution of the original initial boundary value problem.
scientific article; zbMATH DE number 4074730