Almost conservation laws and global rough solutions to a nonlinear Schrödinger equation

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

doi:10.4310/MRL.2002.v9.n5.a9

Almost conservation laws and global rough solutions to a nonlinear Schrödinger equation

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

Mathematics

Research output: Contribution to journal › Article › peer-review

143 Scopus citations

Abstract

We prove an "almost conservation law" to obtain global-in-time well-posedness for the cubic, defocussing nonlinear Schrödinger equation in H^S(ℝⁿ) when n = 2, 3 and s > 4/7, 5/6, respectively.

Original language	English (US)
Pages (from-to)	659-682
Number of pages	24
Journal	Mathematical Research Letters
Volume	9
Issue number	5-6
DOIs	https://doi.org/10.4310/MRL.2002.v9.n5.a9
State	Published - 2002

Keywords

Nonlinear Schrödinger equation
Well-posedness

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title = "Almost conservation laws and global rough solutions to a nonlinear Schr{\"o}dinger equation",

abstract = "We prove an {"}almost conservation law{"} to obtain global-in-time well-posedness for the cubic, defocussing nonlinear Schr{\"o}dinger equation in HS(ℝn) when n = 2, 3 and s > 4/7, 5/6, respectively.",

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author = "J. Colliander and M. Keel and G. Staffilani and H. Takaoka and T. Tao",

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language = "English (US)",

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publisher = "International Press of Boston, Inc.",

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T1 - Almost conservation laws and global rough solutions to a nonlinear Schrödinger equation

AU - Colliander, J.

AU - Keel, M.

AU - Staffilani, G.

AU - Takaoka, H.

AU - Tao, T.

PY - 2002

Y1 - 2002

N2 - We prove an "almost conservation law" to obtain global-in-time well-posedness for the cubic, defocussing nonlinear Schrödinger equation in HS(ℝn) when n = 2, 3 and s > 4/7, 5/6, respectively.

AB - We prove an "almost conservation law" to obtain global-in-time well-posedness for the cubic, defocussing nonlinear Schrödinger equation in HS(ℝn) when n = 2, 3 and s > 4/7, 5/6, respectively.

KW - Nonlinear Schrödinger equation

KW - Well-posedness

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UR - http://www.scopus.com/inward/citedby.url?scp=0036771238&partnerID=8YFLogxK

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DO - 10.4310/MRL.2002.v9.n5.a9

M3 - Article

AN - SCOPUS:0036771238

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VL - 9

SP - 659

EP - 682

JO - Mathematical Research Letters

JF - Mathematical Research Letters

IS - 5-6

ER -

Almost conservation laws and global rough solutions to a nonlinear Schrödinger equation

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Keywords

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