Long time behavior for a dissipative shallow water model

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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.
Original languageEnglish
Pages (from-to)731-757
Number of pages27
JournalANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE
Volume34
Publication statusPublished - 2017

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematical Physics
  • Applied Mathematics

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