Global Strong Solution for Large Data to the Hyperbolic Navier-Stokes Equation

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 the existence of global strong solutions for large data including decay rates in $\mathbb{R}^2$ and in the three dimensional special cases known from the classical Navier-Stokes equation. As a corollary we can derive from [Sch12] a global relaxation limit $\tau \to 0$ uniform in time. Furthermore we give an improved version of the regularity criterion of [FO12].