On The Isothermal Compressible Multi-component Mixture Flow: The Local Existence And Maximal Lp − Lq Regularity Of Solutions

We consider the initial-boundary value problem for the system of equations describing the flow of compressible isothermal mixture of arbitrary large number of components. The system consists of the compressible Navier-Stokes equations and a subsystem of diffusion equations for the species. The subsystems are coupled by the form of the pressure and the strong cross-diffusion effects in the diffusion fluxes of the species. Assuming the existence of solutions to the symmetrized and linearized equations, proven in [31], we derive the estimates for the nonlinear equations and prove the local-in-time existence and maximal Lp − Lq regularity of solutions