Large-time behavior of viscous surface waves

We consider the mathematical behavior of a viscous, incompressible fluid bounded above by an atmosphere of constant pressure and below by a horizontal bottom. After reviewing the existence and regularity theory for the equations governing the motion, we establish rates of decay for solutions near equilibrium. The function describing the height of the free surface decays like 1/square root of t; the velocity field decays like 1/t. These estimates are shown first for the linearization about equilibrium and then for the full nonlinear problem. Complete details will be given elsewhere.