Stability of shock waves in magnetohydrodynamics
We discuss the question of the possibility of the construction of examples of ill-posedness of the Hadamard type for mixed problems on the stability of fast and slow magnetohydrodynamic shock waves. For a polytropic gas we investigate the stability of a fast magnetohydrodynamic shock wave for a weak magnetic field and the stability of a slow magnetohydrodynamic shock wave for a strong magnetic field. For the last case we construct an example of ill-posedness of the Hadamard type, showing the instability of this type of shock wave (under strong magnetic fields).
stability of fast and slow magnetohydrodynamic shock waves
scientific article; zbMATH DE number 4172654