The Defocusing Ḣ¹ᐟ²-Critical NLS in High Dimensions
We consider the defocusing Ḣ1/2-critical nonlinear Schrödinger equation in dimensions d ≥ 4. In the spirit of Kenig and Merle , we combine a concentration-compactness approach with the Lin-Strauss Morawetz inequality to prove that if a solution u is bounded in Ḣ1/2 throughout its lifespan, then u is global and scatters.
J. Murphy, "The Defocusing Ḣ¹ᐟ²-Critical NLS in High Dimensions," Discrete and Continuous Dynamical Systems- Series A, vol. 34, no. 2, pp. 733 - 748, American Institute of Mathematical Sciences (AIMS), Feb 2014.
The definitive version is available at https://doi.org/10.3934/dcds.2014.34.733
Mathematics and Statistics
Keywords and Phrases
Concentration-compactness; Ḣ1/2-critical; Lin-Strauss Morawetz inequality; Nonlinear Schrödinger equation; Scattering
International Standard Serial Number (ISSN)
Article - Journal
© 2014 American Institute of Mathematical Sciences (AIMS), All rights reserved.
01 Feb 2014