Global existence and scattering for rough solutions of a nonlinear Schrödinger equation on ℝ 3

J. Colliander, M. Keel, G. Staffilani, H. Takaoka, T. Tao

Research output: Contribution to journalArticlepeer-review

130 Scopus citations

Abstract

We prove global existence and scattering for the defocusing, cubic, nonlinear Schrödinger equation in H S(ℝ 3) for s > 4/5. The main new estimate in the argument is a Morawetz-type inequality for the solution φ. This estimate bounds ||φ(x,t)|| L x,t4(ℝ 3×ℝ), whereas the well-known Morawetz-fype estimate of Lin-Strauss controls ∫ 0 ℝ3 (φ(x,t)) 4/|x| dx dt.

Original languageEnglish (US)
Pages (from-to)987-1014
Number of pages28
JournalCommunications on Pure and Applied Mathematics
Volume57
Issue number8
DOIs
StatePublished - Aug 1 2004

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