article published yes Rowan Killip author Tadahiro Oh author Oana Pocovnicu author Monica Visan author 056daca0-b8d1-11f0-964f-f91054abf8ca 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. International Press of Boston2013 eng NLSGross–Pitaevskii equationnon-vanishing boundary condition 1073-2780 1945-001X 1112.135410.4310/mrl.2012.v19.n5.a1 195969-986 yes Killip, Rowan, Tadahiro Oh, Oana Pocovnicu, and Monica Vişan. “Global Well-Posedness of the Gross–Pitaevskii and Cubic-Quintic Nonlinear Schrödinger Equations with Non-Vanishing Boundary Conditions.” <i>Mathematical Research Letters</i>. International Press of Boston, 2013. <a href="https://doi.org/10.4310/mrl.2012.v19.n5.a1">https://doi.org/10.4310/mrl.2012.v19.n5.a1</a>. Killip R, Oh T, Pocovnicu O, Vişan M. Global well-posedness of the Gross–Pitaevskii and cubic-quintic nonlinear Schrödinger equations with non-vanishing boundary conditions. <i>Mathematical Research Letters</i>. 2013;19(5):969-986. doi:<a href="https://doi.org/10.4310/mrl.2012.v19.n5.a1">10.4310/mrl.2012.v19.n5.a1</a> R. Killip, T. Oh, O. Pocovnicu, and M. Vişan, “Global well-posedness of the Gross–Pitaevskii and cubic-quintic nonlinear Schrödinger equations with non-vanishing boundary conditions,” <i>Mathematical Research Letters</i>, vol. 19, no. 5. International Press of Boston, pp. 969–986, 2013. Killip, Rowan, et al. “Global Well-Posedness of the Gross–Pitaevskii and Cubic-Quintic Nonlinear Schrödinger Equations with Non-Vanishing Boundary Conditions.” <i>Mathematical Research Letters</i>, vol. 19, no. 5, International Press of Boston, 2013, pp. 969–86, doi:<a href="https://doi.org/10.4310/mrl.2012.v19.n5.a1">10.4310/mrl.2012.v19.n5.a1</a>. R. Killip, T. Oh, O. Pocovnicu, M. Vişan, Mathematical Research Letters 19 (2013) 969–986. Killip, R., Oh, T., Pocovnicu, O., &#38; Vişan, M. (2013). Global well-posedness of the Gross–Pitaevskii and cubic-quintic nonlinear Schrödinger equations with non-vanishing boundary conditions. <i>Mathematical Research Letters</i>. International Press of Boston. <a href="https://doi.org/10.4310/mrl.2012.v19.n5.a1">https://doi.org/10.4310/mrl.2012.v19.n5.a1</a> Killip R, Oh T, Pocovnicu O, Vişan M. 2013. 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. 220532026-06-19T07:54:49Z2026-06-25T08:33:18Z