A quasilinear delayed hyperbolic Navier-Stokes system: global solution, asymptotics and relaxation limit

We consider a hyperbolic quasilinear fluid model, that arises from a delayed version for the constitutive law for the deformation tensor in the incompressible Navier-Stokes equation. We prove global existence of small solutions and asymptotic results in $R^3$ and the half-space with slip boundary conditions. Futhermore we show that this relaxed system is close to the classical Navier-Stokes equation in the sense that for small times t the solutions converge in high Sobolev norms to the solution of the incompressible Navier-Stokes equation.

Keywords

Navier-Stokes, global small solution, decay rate, Cattaneo law, Fourier law, Oldroyd, relaxation limit, delay equation

2010 Mathematics Subject Classification

35B40, 35L72, 35Q30, 35Q35, 76D05

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Published 10 December 2012