Resonant decompositions and the I-method for cubic nonlinear Schrodinger on R^2

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dc.creatorColliander, J.
dc.creatorKeel, M.
dc.creatorStaffilani, G.
dc.creatorTakaoka, H.
dc.creatorTao, T.
dc.date2007-04-20
dc.date.accessioned2026-07-07T07:57:37Z
dc.date.available2026-07-07T07:57:37Z
dc.descriptionThe initial value problem for the cubic defocusing nonlinear Schrödinger equation $i \partial_t u + Δu = |u|^2 u$ on the plane is shown to be globally well-posed for initial data in $H^s (\R^2)$ provided $s>1/2$. The proof relies upon an almost conserved quantity constructed using multilinear correction terms. The main new difficulty is to control the contribution of resonant interactions to these correction terms. The resonant interactions are significant due to the multidimensional setting of the problem and some orthogonality issues which arise.
dc.identifierhttps://arxiv.org/abs/0704.2730
dc.identifierhttp://arxiv.org/abs/0704.2730
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/127711
dc.subjectAnalysis of PDEs
dc.subjectMathematical Physics
dc.subject35Q55
dc.titleResonant decompositions and the I-method for cubic nonlinear Schrodinger on R^2
dc.typetext

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