A priori bounds and weak solutions for the nonlinear Schrödinger equation in Sobolev spaces of negative order

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dc.creatorChrist, Michael
dc.creatorColliander, James
dc.creatorTao, Terence
dc.date2006-12-15
dc.date.accessioned2026-07-07T07:35:40Z
dc.date.available2026-07-07T07:35:40Z
dc.descriptionSolutions to the Cauchy problem for the one-dimensional cubic nonlinear Schrödinger equation on the real line are studied in Sobolev spaces $H^s$, for $s$ negative but close to 0. For smooth solutions there is an {\em a priori} upper bound for the $H^s$ norm of the solution, in terms of the $H^s$ norm of the datum, for arbitrarily large data, for sufficiently short time. Weak solutions are constructed for arbitrary initial data in $H^s$.
dc.description22 pages
dc.identifierhttps://arxiv.org/abs/math/0612457
dc.identifierhttp://arxiv.org/abs/math/0612457
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/120168
dc.subjectAnalysis of PDEs
dc.subject35Q55
dc.titleA priori bounds and weak solutions for the nonlinear Schrödinger equation in Sobolev spaces of negative order
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