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

Under consideration is the inhomogeneous boundary value problem for the equations of a mixture of viscous compressible fluids modelling a steady flow around an obstacle. The statement of the problem presumes the possibility of varying the shape of obstacle. The well-posedness of such a problemin the class of strong solutions is proved. The results of the paper can be used for analyzing the optimal shape of an obstacle under a flow around it by a mixture of compressible viscous fluids. © 2015, Pleiades Publishing, Ltd.