Exponential attractors for non-dissipative systems modeling convection in porous media
Pierre Fabrie, B. Nicolaenko · Asymptotic Analysis · 1996
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.