Global well-posedness of the Gross–Pitaevskii and cubic-quintic nonlinear Schrödinger equations with non-vanishing boundary conditions Killip, Rowan Oh, Tadahiro Pocovnicu, Oana Visan, Monica NLS Gross–Pitaevskii equation non-vanishing boundary condition 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 Boston 2013 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/22053 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> eng info:eu-repo/semantics/altIdentifier/doi/10.4310/mrl.2012.v19.n5.a1 info:eu-repo/semantics/altIdentifier/issn/1073-2780 info:eu-repo/semantics/altIdentifier/e-issn/1945-001X info:eu-repo/semantics/altIdentifier/arxiv/1112.1354 info:eu-repo/semantics/openAccess