English

Well-posedness of a water wave model with viscous effects

Analysis of PDEs 2020-04-01 v3 Fluid Dynamics

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 well-posedness in Sobolev spaces of such equation.

Keywords

Cite

@article{arxiv.1911.01912,
  title  = {Well-posedness of a water wave model with viscous effects},
  author = {Rafael Granero-Belinchón and Stefano Scrobogna},
  journal= {arXiv preprint arXiv:1911.01912},
  year   = {2020}
}