Wellposedness of a water wave model with viscous effects
Abstract
Starting from the paper by Dias, Dyachenko and Zakharov (\emph{Physics Letters A, 2008}) on viscous water waves, we derive a model that describes water waves with viscosity moving in deep water with or without surface tension effects. This equation takes the form of a nonlocal fourth order wave equation and retains the main contributions to the dynamics of the free surface. Then, we prove the wellposedness in Sobolev spaces of such equation.
 Publication:

arXiv eprints
 Pub Date:
 November 2019
 arXiv:
 arXiv:1911.01912
 Bibcode:
 2019arXiv191101912G
 Keywords:

 Mathematics  Analysis of PDEs;
 Physics  Fluid Dynamics