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Feireisl, E.; Liao, X.; Málek, J.

Global weak solutions to a class of non-Newtonian compressible fluids. (English) Zbl 1335.35180

Math. Methods Appl. Sci. 38, No. 16, 3482-3494 (2015).
Summary: We consider a class of compressible fluids with nonlinear constitutive equations that guarantee that the divergence of the velocity field remains bounded. We study mathematical properties of unsteady three-dimensional flows of such fluids in bounded domains. In particular, we show the long-time and large-data existence result of weak solutions with strictly positive density.

Cited in 1 Review
Cited in 20 Documents

MSC:

35Q30 Navier-Stokes equations
76A05 Non-Newtonian fluids
35D30 Weak solutions to PDEs
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics

Keywords:

compressible fluid; generalized Newtonian fluids; power law fluid; bounded divergence of the velocity; weak solutions; positive density
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References:

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