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

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


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