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

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dc.creatorColliander, J.
dc.creatorKeel, M.
dc.creatorStaffilani, G.
dc.creatorTakaoka, H.
dc.creatorTao, T.
dc.date2003-01-23
dc.date2004-04-06
dc.date.accessioned2026-07-07T04:54:38Z
dc.date.available2026-07-07T04:54:38Z
dc.descriptionWe prove global existence and scattering for the defocusing, cubic nonlinear Schrödinger equation in $H^s(\rr^3)$ for $s > {4/5}$. The main new estimate in the argument is a Morawetz-type inequality for the solution $ϕ$. This estimate bounds $\|ϕ(x,t)\|_{L^4_{x,t}(\rr^3 \times \rr)}$, whereas the well-known Morawetz-type estimate of Lin-Strauss controls $\int_0^{\infty}\int_{\rr^3}\frac{(ϕ(x,t))^4}{|x|} dx dt
dc.descriptionFinal version, to appear in Communications on Pure and Applied Mathematics: typos fixed, some expository remarks and references added, referee's suggestions incorporated
dc.identifierhttps://arxiv.org/abs/math/0301260
dc.identifierhttp://arxiv.org/abs/math/0301260
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/66332
dc.subjectAnalysis of PDEs
dc.titleGlobal existence and scattering for rough solutions of a nonlinear Schroedinger equation on R^3
dc.typetext

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