### 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 language | English |
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Pages (from-to) | 969-986 |

Number of pages | 18 |

Journal | Mathematical Research Letters |

Volume | 19 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2012 |

### Keywords

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

## Cite this

Killip, R., Oh, T., Pocovnicu, O., & Visan, M. (2012). Global well-posedness of the Gross–Pitaevskii and cubic-quintic nonlinear Schrödinger equations with non-vanishing boundary conditions.

*Mathematical Research Letters*,*19*(5), 969-986. https://doi.org/10.4310/MRL.2012.v19.n5.a1