JournalsjstVol. 6, No. 3pp. 429–481

Global well-posedness and long-time asymptotics for the defocussing Davey–Stewartson II equation in H1,1(C)H^{1,1}(\mathbb 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

A subscription is required to access this article.

Abstract

We use the ˉ\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 tt \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 H1,1(C)H^{1,1}(\mathbb C). J. Spectr. Theory 6 (2016), no. 3, pp. 429–481

DOI 10.4171/JST/129