CONDITIONAL REGULARITY FOR THE COMPRESSIBLE MHD SYSTEM WITH INHOMOGENEOUS BOUNDARY DATA\ast

1. Introduction. The present paper is a continuation of our work concerning conditional regularity of solutions to open systems arising in fluid dynamics; see [2]. The results can be seen as another evidence supporting the celebrated Nash's conjecProbably one should first try to prove a conditional existence and uniqueness theorem for flow equations. This should give existence, smoothness, and unique continuation (in time) of flows, conditional on the nonappearance of certain gross types of singularity, such as infinities of temperature or density. This principle can be stated in a more concise way: