On the isothermal compressible multi-component mixture flow: The local existence and maximal Lp−Lq regularity of solutions. (December 2019) - Piasecki, T.; Shibata, Y.; Zatorska, E.
Abstract: 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 Piasecki, Shibata and Zatorska (2019), we derive the estimates for the nonlinear equations and prove the local-in-time existence and maximal L p − L q regularity of solutions.