6533b852fe1ef96bd12aac82

RESEARCH PRODUCT

Long time behavior for a dissipative shallow water model

Maria E. SchonbekMarco SammartinoVincenzo Sciacca

subject

Inertial frame of referenceFourier splitting methodDynamical Systems (math.DS)Space (mathematics)Dynamical system01 natural sciencesPhysics::Fluid DynamicsNavier–Stokes equationsMathematics - Analysis of PDEsAttractorFOS: MathematicsMathematics - Dynamical Systems0101 mathematicsNavier–Stokes equationsPhysics::Atmospheric and Oceanic PhysicsMathematical PhysicsMathematicsApplied Mathematics010102 general mathematicsMathematical analysisAttractorIncompressible viscous fluidInertial manifoldFunctional Analysis (math.FA)Mathematics - Functional Analysis010101 applied mathematicsWaves and shallow waterTime decayDissipative systemCompressibilityAnalysisAnalysis of PDEs (math.AP)

description

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.

yearjournalcountryeditionlanguage
2013-10-30Annales de l'Institut Henri Poincaré C, Analyse non linéaire
https://doi.org/10.1016/j.anihpc.2016.05.003