  In this paper we study the regularity properties of solutions to the
Davey-Stewartson system. It is shown that for initial data in a Sobolev space,
the nonlinear part of the solution flow resides in a smoother space than the
initial data for all times. We also obtain that the Sobolev norm of the
nonlinear part of the evolution grows at most polynomially. As an application
of the smoothing estimate, we study the long term dynamics of the forced and
weakly damped Davey-Stewartson system. In this regard we give a new proof for
the existence and smoothness of the global attractors in the energy space.
