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Large amplitude variations for the density of a viscous compressible fluid. (Variations de grande amplitude pour la densité d’un fluide visqueux compressible.) (French) Zbl 0739.35071
Summary: 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.

35Q30 Navier-Stokes equations
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
35M10 PDEs of mixed type
Full Text: DOI
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