LOCAL STRONG SOLUTION TO THE COMPRESSIBLE MAGNETOHYDRODYNAMIC FLOW WITH LARGE DATA

Abstract

The three-dimensional compressible magnetohydrodynamic isentropic flow with zero magnetic diffusivity is studied in this paper. The vanishing magnetic diffusivity causes significant difficulties due to the loss of dissipation of the magnetic field. The existence and uniqueness of local-in-time strong solutions with large initial data is established. Strong solutions have weaker regularity than classical solutions. A generalized Lax–Milgram theorem and a Schauder–Tychonoff-type fixed-point argument are applied on conjunction with novel techniques and estimates for strong solutions.