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Hyperbolic Navier-Stokes equations I: Local well-posedness
June 2012, 1(1): 217-234. doi: 10.3934/eect.2012.1.217
Hyperbolic Navier-Stokes equations II: Global existence of small solutions
Reinhard Racke 1, and Jürgen Saal 2,
Department of Mathematics, University of Konstanz, 78457 Konstanz
Center of Smart Interfaces, Technische Universität Darmstadt, Petersenstraße 32, 64287 Darmstadt
Received September 2011 Revised December 2011 Published March 2012
We consider a hyperbolicly perturbed Navier-Stokes initial value problem in ${\mathbb R}^n$, $n=2,3$, arising from using a Cattaneo type relation instead of a Fourier type one in the constitutive equations. The resulting system is an essentially hyperbolic one with quasilinear nonlinearities. The global existence of smooth solutions for small data is proved, and relations to the classical Navier-Stokes systems are discussed.
Keywords: decay rate, Oldroyd, Navier-Stokes, Cattaneo law, Fourier law, global small solution, blow-up..
Mathematics Subject Classification: Primary: 35L72, 35Q30, 76D0.
Citation: Reinhard Racke, Jürgen Saal. Hyperbolic Navier-Stokes equations II: Global existence of small solutions. Evolution Equations & Control Theory, 2012, 1 (1) : 217-234. doi: 10.3934/eect.2012.1.217
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Reinhard Racke Jürgen Saal