Large data mass-subcritical NLS: critical weighted bounds imply scattering

We consider the mass-subcritical nonlinear Schrödinger equation in all space dimensions with focusing or defocusing nonlinearity. For such equations with critical regularity s c ∈ ( max { - 1 , - d 2 } , 0 ) , we prove that any solution satisfying | x | | s c | e - i t Δ u L t ∞ L x 2 < ∞ on its...

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Bibliographic Details
Published inNonlinear differential equations and applications Vol. 24; no. 4
Main Authors Killip, Rowan, Masaki, Satoshi, Murphy, Jason, Visan, Monica
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.08.2017
Springer Nature B.V
Subjects
Analysis
Defocusing
Mathematical analysis
Mathematics
Mathematics and Statistics
Nonlinearity
Regularity
Scattering
35Q55
Nonlinear Schrödinger equations
Scattering
Concentration compactness
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Summary:We consider the mass-subcritical nonlinear Schrödinger equation in all space dimensions with focusing or defocusing nonlinearity. For such equations with critical regularity s c ∈ ( max { - 1 , - d 2 } , 0 ) , we prove that any solution satisfying | x | | s c | e - i t Δ u L t ∞ L x 2 < ∞ on its maximal interval of existence must be global and scatter.
ISSN:1021-9722
1420-9004
DOI:10.1007/s00030-017-0463-9