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