On well-posedness of inhomogeneous boundary value problem for equations of mixtures of compressible viscous fluids

The inhomogeneous boundary value problem for equations of mixture of compressible viscous fluids which is steady flow around an obstacle model are considered. Problem formulation makes it possible to vary by shape of obstacles. Well-posedness of such problem for class of strong solutions is proved. The results established in the paper can be used to make an analysis of an optimal shape for obstacles in compressible flow of mixture of viscous fluids.