%0 Journal Article
%T Derivation of a viscous Boussinesq system for surface water waves
%A Herv¨¦ Le Meur
%J Mathematics
%D 2013
%I arXiv
%X In this article, we derive a viscous Boussinesq system for surface water waves from Navier-Stokes equations. We use neither the irrotationality assumption, nor the Zakharov-Craig-Sulem formulation. During the derivation, we find the bottom shear stress, and also the decay rate for shallow water. In order to justify our derivation, we derive the viscous Korteweg-de Vries equation from our viscous Boussinesq system and compare it to the ones found in the bibliography. We also extend the system to the 3-D case.
%U http://arxiv.org/abs/1305.6296v2