Global well-posedness and long-time asymptotics for the defocussing Davey-Stewartson II equation in H1,1(ℂ)

Peter A. Perry, Michael Christ

Research output: Contribution to journalReview articlepeer-review

22 Scopus citations


We use the ∂-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 → ∞ in terms of an associated linear problem. These results appear to be sharp.

Original languageEnglish
Pages (from-to)429-481
Number of pages53
JournalJournal of Spectral Theory
Issue number3
StatePublished - 2016

Bibliographical note

Funding Information:
Supported in part by NSF Grants DMS-0710477 and DMS-1208778. Supported in part by NSF grant DMS-0901569. It is a pleasure to thank Russell Brown, Ken McLaughlin, Michael Music, and Peter Topalov for helpful discussions, to thank Russell Brown, Peter Miller, and Katharine Ott for a careful reading of the manuscript, and to thank Michael Christ and Catherine Sulem for helpful correspondence. I am also grateful to the referee for an exceptionally thorough and meticulous reading of three (!) versions of this manuscript, for pointing out several errors in an earlier version of this paper, and for numerous helpful suggestions which have considerably improved the manuscript. The current proof of Lemma 3.11 incorporates a suggestion of the referee. Part of this work was carried out at the Mathematical Sciences Research Institute in Berkeley, California, whose hospitality the author gratefully acknowledges.

Publisher Copyright:
© European Mathematical Society.


  • Davey-Stewartson equation
  • Inverse scattering
  • ∂-method

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Geometry and Topology


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