  The convective transport in a multicomponent isothermal compressible fluid
subject to the mass continuity equations is considered. The velocity is
proportional to the negative pressure gradient, according to Darcy's law, and
the pressure is defined by a state equation imposed by the volume extension of
the mixture. These model assumptions lead to a parabolic-hyperbolic system for
the mass densities. The global-in-time existence of classical and weak
solutions is proved in a bounded domain with no-penetration boundary
conditions. The idea is to decompose the system into a porous-medium-type
equation for the volume extension and transport equations for the modified
number fractions. The existence proof is based on parabolic regularity theory,
the theory of renormalized solutions, and an approximation of the velocity
field.
