Dynamical Behaviour of Rotating Internal Weakly Viscoelastic Fluids

The analytic formulation is discussed of a model introduced by Speziale describing the flow of weakly viscoelastic incompressible fluids in rotating machinery with externally and determined pressure gradient. The equations are expressed in non-dimensional form involving the Reynolds, Rossby and Weissenberg numbers. In a suitable parameter range, existence of solutions is established in suitable function spaces. Using standard theory from infinite dimensional dynamical systems, estimates are given on the Hausdorff dimension of the associated functionally invariant set, finally we introduce the nonlinear Galerkin method associated with a approximate inertial manifold, we determine the rate of convergence of the solutions enter to the approximate inertial manifold as well as the error of the nonlinear Galerkin method.