Bounds for the dimensions of the attractors of non-linear bipolar viscous fluids

Abstract

The existence of a maximal global attractor is demonstrated for the dynamical system generated by the initial boundary value problem associated with the motion of a non-linear bipolar fluid; the attractor has the form A=∩_t>0S(t)B^ρ′_(H²(Ω))³ where S(t) is the relevant non-linear semigroup and B^ρ′_(H²(Ω))³ (the ball of radius ρ′>0 in (H²(Ω))³) is, for ρ′ sufficiently large, an absorbing set. Upper bounds are obtained for the Hausdorff and Fractal dimensions of the attractor A.