Hyperbolic Navier-Stokes equations in three space dimensions

We consider in this paper a hyperbolic quasilinear version of the Navier-Stokes equations three space dimensions, obtained by using Cattaneo type law instead Fourier law. In our earlier work [2], we proved global existence and uniqueness solutions for initial data small enough H4(R3)3 ? H3(R3)3. paper, refine previous result establish under significantly lower regularity. first prove local solution, H5 2 +?(R3)3 ?H32 +?(R3)3, > 0. Under weaker smallness assumptions on forcing term, solutions. Finally, show that if is close to 0, then solution perturbed equation classical equations.