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We consider the initial-boundary value problem for the system of equationsdescribing the flow of compressible isothermal mixture of arbitrary largenumber of components. The system consists of the compressible Navier-Stokesequations and a subsystem of diffusion equations for the species. Thesubsystems are coupled by the form of the pressure and the strongcross-diffusion effects in the diffusion fluxes of the species. Assuming theexistence of solutions to the symmetrized and linearized equations, proven in[35], we derive the estimates for the nonlinear equations and prove thelocal-in-time existence and maximal $L_p-L_q$ regularity of solutions.

On the isothermal compressible multi-component mixture flow: the local existence and maximal $L_p-L_q$ regularity of solutions