Long time behavior for a dissipative shallow water model

Abstract

We consider the two-dimensional shallow water model derived in [29], describing the motion of an incompressible fluid, confined in a shallow basin, with varying bottom topography. We construct the approximate inertial manifolds for the associated dynamical system and estimate its order. Finally, working in the whole space R2, under suitable conditions on the time dependent forcing term, we prove the L2 asymptotic decay of the weak solutions.