We show that the inverse scattering map for the linear system associated with the defocussing Davey-Stewartson II equation is locally Lipschitz continuous with locally Lipschitz continuous inverse on $H^{ 1,1}(R^2)$. From the inverse scattering method we then obtain global well-posedness for the defocussing Davey-Stewartson II equation. We show that these global solutions are dispersive by computing their leading asymptotic behavior as $t \rightarrow \infty$ in terms of an associated linear problem.
Categories: math.AP math.SP