We consider the two-dimensional shallow water model derived in , 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 R^2, under suitable conditions on the time dependent forcing term, we prove the L^2 asymptotic decay of the weak solutions.
|Number of pages||27|
|Journal||ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE|
|Publication status||Published - 2017|
All Science Journal Classification (ASJC) codes
- Mathematical Physics
- Applied Mathematics