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

Article type: Research Article

Authors: Bellout, Hamid | Bloom, Frederick^; | Nečas, Jindrich^;

Affiliations: Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL 60115, USA | Mathematical Institute, Charles University, Prague, Czechoslovakia

Note: [] Research supported, in part, by ONR Grant NOOOI4-91-J-1002

Note: [] Currently in the Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL 60115, USA

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)Bρ′(H2(Ω))3 where S(t) is the relevant non-linear semigroup and Bρ′(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.

DOI: 10.3233/ASY-1995-11202

Journal: Asymptotic Analysis, vol. 11, no. 2, pp. 131-167, 1995