The Radial Defocusing Nonlinear Schrödinger Equation in Three Space Dimensions
We study the defocusing nonlinear Schrödinger equation in three space dimensions. We prove that any radial solution that remains bounded in the critical Sobolev space must be global and scatter. In the energy-supercritical setting we employ a space-localized Lin-Strauss Morawetz inequality of Bourgain. In the intercritical regime we prove long-time Strichartz estimates and frequency-localized Lin-Strauss Morawetz inequalities.
J. Murphy, "The Radial Defocusing Nonlinear Schrödinger Equation in Three Space Dimensions," Communications in Partial Differential Equations, vol. 40, no. 2, pp. 265 - 308, Taylor & Francis, Feb 2015.
The definitive version is available at https://doi.org/10.1080/03605302.2014.949379
Mathematics and Statistics
Keywords and Phrases
Concentration-compactness; Lin-Strauss Morawetz inequality; Nonlinear Schrödinger equation; Scattering
International Standard Serial Number (ISSN)
Article - Journal
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01 Feb 2015