Domain dependence of solutions to the boundary value problem for equations of mixtures of compressible viscous fluids

Abstract

Under study is the dependence of solutions of an inhomogeneous boundary value problem for a system of equations of mixtures of compressible viscous fluids on the shape of the flow domain. The obtained results can be used to proof the differentiability of solutions and functionals of the solutions (e.g., the drag functional) with respect to a parameter that characterizes the shape variations of an obstacle in the flow.