  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.
