Global well-posedness and long-time asymptotics for the defocussing Davey–Stewartson II equation in $H^{1,1}(\mathbb{C})$

Abstract

We use the $\bar{\partial }$-inverse scattering method to obtain global well-posedness and large-time asymptotics for the defocussing Davey–Stewartson II equation. We show that these global solutions are dispersive by computing their leading asymptotic behavior as $t\to \infty$ in terms of an associated linear problem. These results appear to be sharp.