Global well-posedness of the Gross–Pitaevskii and cubic-quintic nonlinear Schrödinger equations with non-vanishing boundary conditions
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.
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Author
Killip, Rowan;
Oh, Tadahiro;
Pocovnicu, Oana;
Vişan, MonicaISTA
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.
Mathematics Subject Classification
Publishing Year
Date Published
2013-03-15
Journal Title
Mathematical Research Letters
Publisher
International Press of Boston
Volume
19
Issue
5
Page
969-986
ISSN
eISSN
IST-REx-ID
Cite this
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. Mathematical Research Letters. 2013;19(5):969-986. doi:10.4310/mrl.2012.v19.n5.a1
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. International Press of Boston. https://doi.org/10.4310/mrl.2012.v19.n5.a1
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.” Mathematical Research Letters. International Press of Boston, 2013. https://doi.org/10.4310/mrl.2012.v19.n5.a1.
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,” Mathematical Research Letters, vol. 19, no. 5. International Press of Boston, pp. 969–986, 2013.
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.
Killip, Rowan, et al. “Global Well-Posedness of the Gross–Pitaevskii and Cubic-Quintic Nonlinear Schrödinger Equations with Non-Vanishing Boundary Conditions.” Mathematical Research Letters, vol. 19, no. 5, International Press of Boston, 2013, pp. 969–86, doi:10.4310/mrl.2012.v19.n5.a1.
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