A refined global well-posedness result for Schrodinger equations with derivative

Simple item page
dc.creatorColliander, J.
dc.creatorKeel, M.
dc.creatorStaffilani, G.
dc.creatorTakaoka, H.
dc.creatorTao, T.
dc.date2001-10-02
dc.date2002-02-27
dc.date.accessioned2026-07-07T04:43:37Z
dc.date.available2026-07-07T04:43:37Z
dc.descriptionIn this paper we prove that the 1D Schrödinger equation with derivative in the nonlinear term is globally well-posed in $H^{s}$, for $s>\frac12$ for data small in $L^{2}$. To understand the strength of this result one should recall that for $s<\frac12$ the Cauchy problem is ill-posed, in the sense that uniform continuity with respect to the initial data fails. The result follows from the method of almost conserved energies, an evolution of the ``I-method'' used by the same authors to obtain global well-posedness for $s>\frac23$. The same argument can be used to prove that any quintic nonlinear defocusing Schrödinger equation on the line is globally well-posed for large data in $H^{s}$, for $s>\frac12$.
dc.description21 pages, no figures, submitted, Siam J. Math
dc.identifierhttps://arxiv.org/abs/math/0110026
dc.identifierhttp://arxiv.org/abs/math/0110026
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/62301
dc.subjectAnalysis of PDEs
dc.subject35Q55
dc.titleA refined global well-posedness result for Schrodinger equations with derivative
dc.typetext

Files

Collections

arXiv