Derivation of a viscous Boussinesq system for surface water waves

作者：Le Meur Herve V J^*

来源：Asymptotic Analysis, 2015, 94(3-4): 309-345.

DOI：10.3233/ASY-151315

• water waves
• shallow water
• Boussinesq system
• viscosity
• KdV equation

In this article, we derive a viscous Boussinesq system for surface water waves from Navier-Stokes equations for non-vanishing initial conditions. The relevance of such initial conditions is proved. 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 3D geometry.

• 出版日期2015