Global smoothing for the Davey–Stewartson system on $$\mathbb {R}^2$$

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