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

Analysis of PDEs