CLASS OF NON-NEWTONIAN FLUIDS - AQUEOUS POLYMER-SOLUTIONS

The aim of this paper is to study a nonlinear evolution system of third order representing an approximation of Navier-Stokes equations. This system describes the motion of a viscous fluid to which a small quantity of polymers is added. The consequently main relaxation properties of the resulting fluid are completely changed. We consider the case of a smooth open bounded set of R(n), n = 2 or 3, and show the existence and the uniqueness of a solution, local in time, for sufficiently regular data (the initial velocity u0 is-an-element-of H-3, the external force f is-an-element-of L2(0, T; H-1)). The basic tool is a suitable special basis to be used in the Galerkin method. In a special class of functions, we give a uniqueness criterium (but where the existence is not ensured).