Decay of solutions to a water wave model with a nonlocal viscous dispersive term

Olivier Goubet (1) , Louis Dupaigne (1) , Serge Dumont (1) , Min Chen (2)

1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352
2 Purdue University [West Lafayette]

In this article, we investigate a KdV water wave model with a nonlocal viscous term (time half derivative). The wellposedness of the equation and the decay rate of solutions are investigated theoretically and numerically.

Mots clés: nonlocal; long-time asymptotics.; viscous asymptotic models; Nonlinear water waves

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]

Olivier Goubet, Louis Dupaigne, Serge Dumont, Min Chen. Decay of solutions to a water wave model with a nonlocal viscous dispersive term. Discrete and Continuous Dynamical Systems - Series A, 2010, 27 (4), pp.1473-1492. ⟨10.3934/dcds.2010.27.1473⟩. ⟨hal-01113773⟩