Contents Online
Mathematical Research Letters
Volume 19 (2012)
Number 5
Global well-posedness of the Gross–Pitaevskii and cubic-quintic nonlinear Schrödinger equations with non-vanishing boundary conditions
Pages: 969 – 986
DOI: https://dx.doi.org/10.4310/MRL.2012.v19.n5.a1
Authors
Abstract
We consider the Gross–Pitaevskii equation on $\mathbb{R}^4$ and the cubic-quintic nonlinear Schrödinger equation (NLS) on $\mathbb{R}^3$ 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.
Keywords
NLS, Gross–Pitaevskii equation, non-vanishing boundary condition
2010 Mathematics Subject Classification
35Q55
Published 15 March 2013