  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].
