# American Institute of Mathematical Sciences

November  2010, 27(4): 1473-1492. doi: 10.3934/dcds.2010.27.1473

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

 1 Department of Mathematics, Purdue University, West Lafayette, IN 47907 2 LAMFA CNRS UMR 6140, Université de Picardie Jules Verne, 33 rue Saint-Leu 80039 Amiens cedex 3 LAMFA CNRS UMR 6140, Université de Picardie Jules Verne, 33 rue Saint-Leu 80039Amiens Cedex 1 4 Universite de Picardie Jules Verne, LAMFA UMR 7352, 33 rue Saint-Leu, 80039 Amiens cedex

Received  July 2009 Revised  January 2010 Published  March 2010

In this article, we investigate a water wave model with a nonlocal viscous term

$u_t+u_x+\beta$uxxx$+\frac{\sqrt{\nu}}{\sqrt{\pi}}\int_0^t \frac{u_t(s)}{\sqrt{t-s}}ds+$uux$=\nu$uxx$.$

The wellposedness of the equation and the decay rate of solutions are investigated theoretically and numerically.

Citation: Min Chen, S. Dumont, Louis Dupaigne, Olivier Goubet. Decay of solutions to a water wave model with a nonlocal viscous dispersive term. Discrete and Continuous Dynamical Systems, 2010, 27 (4) : 1473-1492. doi: 10.3934/dcds.2010.27.1473
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