Large amplitude variations for the density of a compressible viscous fluid.

Abstract The flow of a compressible viscous fluid is governed by the Navier-Stokes equations. This system is of mixed parabolic-hyperbolic type. The hyperbolic part is associated with a linear degeneracy so that initial large-amplitude high-frequency waves can propagate along the particle paths. However, the parabolic part kills the oscillations of the velocity field. We give a formal relaxed (i.e. homogenized) system in any dimension for the Eulerian formulation. In the 1 − d case, we prove the relevance of this system in the equivalent Lagrangian formulation.