Global well-posedness of the Gross–Pitaevskii and cubic-quintic nonlinear Schrödinger equations with non-vanishing boundary conditions

Rowan Killip, Tadahiro Oh, Oana Pocovnicu, Monica Visan

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

We consider the Gross-Pitaevskii equation on R-4 and the cubic-quintic nonlinear Schrodinger equation (NLS) on R-3 with non-vanishing boundary conditions at spatial infinity. By viewing these equations as perturbations to the energy-critical NLS, we prove that they are globally well-posed in their energy spaces. In particular, we prove unconditional uniqueness in the energy spaces for these equations.

Original languageEnglish
Pages (from-to)969-986
Number of pages18
JournalMathematical Research Letters
Volume19
Issue number5
DOIs
Publication statusPublished - 2012

Keywords

  • NLS; Gross-Pitaevskii equation
  • non-vanishing boundary condition
  • EVOLUTION-EQUATIONS
  • TRAVELING-WAVES
  • 3 DIMENSIONS
  • SCATTERING
  • VORTEX
  • POINT

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