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 R^2, under suitable conditions on the time dependent forcing term, we prove the L^2 asymptotic decay of the weak solutions.
Sciacca, V., Schonbek, M.E., Sammartino, M. (2017). Long time behavior for a dissipative shallow water model. ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE, 34(3), 731-757 [10.1016/j.anihpc.2016.05.003].
Long time behavior for a dissipative shallow water model
SCIACCA, Vincenzo;SAMMARTINO, Marco Maria Luigi
2017-01-01
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 R^2, under suitable conditions on the time dependent forcing term, we prove the L^2 asymptotic decay of the weak solutions.
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