Long time behavior for a dissipative shallow water model
Analysis of PDEs
2015-04-14 v2 Dynamical Systems
Functional Analysis
Abstract
We consider the two-dimensional shallow water model derived by Levermore and Sammartino (Nonlinearity 14,2001), 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, considering the whole domain R^2 and under suitable conditions on the time dependent forcing term, we prove the L^2 asymptotic decay of the weak solutions.
Cite
@article{arxiv.1310.8174,
title = {Long time behavior for a dissipative shallow water model},
author = {Vincenzo Sciacca and Maria E. Schonbek and Marco Sammartino},
journal= {arXiv preprint arXiv:1310.8174},
year = {2015}
}