@article{22053,
  abstract     = {We consider the Gross–Pitaevskii equation on R^4 and the cubic-quintic nonlinear Schrödinger 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.},
  author       = {Killip, Rowan and Oh, Tadahiro and Pocovnicu, Oana and Visan, Monica},
  issn         = {1945-001X},
  journal      = {Mathematical Research Letters},
  keywords     = {NLS, Gross–Pitaevskii equation, non-vanishing boundary condition},
  number       = {5},
  pages        = {969--986},
  publisher    = {International Press of Boston},
  title        = {{Global well-posedness of the Gross–Pitaevskii and cubic-quintic nonlinear Schrödinger equations with non-vanishing boundary conditions}},
  doi          = {10.4310/mrl.2012.v19.n5.a1},
  volume       = {19},
  year         = {2013},
}