Local solvability of equations of magnetohydrodynamics on the whole space

Abstract

Using the technique of expanding domains, we prove the existence of a weak, local in time solution to the equations of magnetohydrodynamics, derived from the equations for viscous, compressible and heat-conducting fluids, on the whole space under special assumptions on pressure and entropy. Compared with the same approach for barotropic compressible fluids, we show how to overcome loss of the global integrability of temperature and velocity fields in corresponding spaces.