Search results for "Inertial manifold"

showing 2 items of 2 documents

Long time behavior for a dissipative shallow water model

2013

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.

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)Annales de l'Institut Henri Poincaré C, Analyse non linéaire
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APPROXIMATE INERTIAL MANIFOLDS FOR THERMODIFFUSION EQUATIONS

2004

In this paper, we consider the two dimensional equations of thermohydraulics, i.e. the coupled system of equations of fluid and temperature in the Boussinesq approximation. We construct a family of approximate Inertial Manifolds whose order decreases exponentially fast with respect to the dimension of the manifold. We give the explicit expression of the order of the constructed manifolds.

PhysicsInertial frame of referenceBenard problem inertial manifolds attractors dissipative systemsMathematical analysisSettore MAT/07 - Fisica MatematicaWaves and Stability in Continuous Media
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