Affiliations: Mathématiques Appliquées, Université Bordeaux I, 33405 Talence Cedex, et L.E.P.T.-ENSAM, URA 873, France | Department of Mathematics, Arizona State University, Tempe, AZ 85287-1804, USA, et INLN, Université de Nice-Sophia Antipolis, France
Note: [] Correspondence to: P. Fabrie, Laboratoire de Mathématiques Appliquées de Bordeaux, Université Bordeaux I, 33405 Talence, France.
Abstract: We consider a system of equations for natural convection in an porous medium, with Darcy's law for the momentum equation. Such a system is only partially dissipative; we establish the existence of an exponential attractor (inertial set) and we obtain estimates for its fractal dimension. The main difficulty lies in the lack of compactness of the corresponding semi group. We show strong continuity of the exponential attractors for a singular limit of the convection model.
