Hyperbolic Navier-Stokes equations II: Global existence of small solutions

Reinhard Racke; Jürgen Saal

doi:10.3934/eect.2012.1.217

Article Contents

2012, Volume 1, Issue 1: 217-234. Doi: 10.3934/eect.2012.1.217

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Hyperbolic Navier-Stokes equations II: Global existence of small solutions

Reinhard Racke^1, and
Jürgen Saal^2,

1.
Department of Mathematics, University of Konstanz, 78457 Konstanz
2.
Center of Smart Interfaces, Technische Universität Darmstadt, Petersenstraße 32, 64287 Darmstadt

Received: September 2011

Revised: December 2011

Published: June 2012

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Abstract

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.

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Mathematics Subject Classification: Primary: 35L72, 35Q30, 76D05.

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