Mass transport in multicomponent compressible fluids: Local and global well-posedness in classes of strong solutions for general class-one models

We consider a system of partial differential equations describing mass transport in multicomponent isothermal compressible fluid. The diffusion fluxes obey the Fick–Onsager or Maxwell–Stefan closure approach. Mechanical forces result into one single convective mixture velocity, barycentric one, which obeys Navier–Stokes equations. thermodynamic pressure is defined by Gibbs–Duhem equation. Chemical potentials and are derived from potential, Helmholtz free energy, with bulk density allowed to be general convex function densities constituents. resulting PDEs mixed parabolic–hyperbolic type. prove two theoretical results concerning well-posedness model classes strong solutions: 1. solution always exists unique for short-times 2. If initial data sufficiently near an equilibrium solution, valid on arbitrary large, but finite time intervals. Both rely contraction principle systems type that behave like linearised parabolic part operator possesses self map property respect some closed ball state space, while being contractive lower order norm only. In this paper, we implement these ideas means precise priori estimates spaces exact regularity.