Intercritical NLS: Critical Ḣˢ-Bounds Imply Scattering
We consider a class of power-type nonlinear Schrödinger equations for which the power of the nonlinearity lies between the mass-and energy-critical exponents. Following the concentration-compactness approach, we prove that if a solution u is bounded in the critical Sobolev space throughout its lifespan, that is, u ∈ Lt∞ Ḣxsc, then u is global and scatters.
J. Murphy, "Intercritical NLS: Critical Ḣˢ-Bounds Imply Scattering," SIAM Journal on Mathematical Analysis, vol. 46, no. 1, pp. 939 - 997, Society for Industrial and Applied Mathematics (SIAM), Jan 2014.
The definitive version is available at https://doi.org/10.1137/120898280
Mathematics and Statistics
Keywords and Phrases
Dinger equation; Intercritical; Life span; NLS; Nonlinear equations; Scattering; Concentration compactness; Intercritical; NLS; Scattering
International Standard Serial Number (ISSN)
Article - Journal
© 2014 Society for Industrial and Applied Mathematics (SIAM), All rights reserved.
01 Jan 2014