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

Peter A. Perry

doi:10.4171/jst/129

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

Peter A. Perry
University of Kentucky, Lexington, USA

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

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Abstract

We use the $\overset{ˉ}{\partial}$ -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.

Cite this article

Peter A. Perry, Global well-posedness and long-time asymptotics for the defocussing Davey–Stewartson II equation in $H^{1, 1} (C)$ . J. Spectr. Theory 6 (2016), no. 3, pp. 429–481

DOI 10.4171/JST/129