  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
[35], we derive the estimates for the nonlinear equations and prove the
local-in-time existence and maximal $L_p-L_q$ regularity of solutions.
