We are concerned with the mathematical derivation of the inhomogeneous
incompressible Navier–Stokes equations (INS) from the compressible Navier–Stokes
equations (CNS) in the large volume viscosity limit. We first prove a result of
large-time existence of regular solutions for (CNS). Next, as a consequence, we
establish that the solutions of (CNS) converge to those of (INS) when the volume
viscosity tends to infinity. Analysis is performed in the two-dimensional torus
for
general initial data. Compared to prior works, the main breakthrough is that we are
able to handle
large variations of density.
Keywords
compressible Navier–Stokes equations, inhomogeneous fluids,
large volume viscosity limit
