Space-time analytic smoothing effect for the pseudo-conformally invariant Schrödinger equations

Gaku Hoshino; Tohru Ozawa

doi:10.1007/s00030-016-0362-5

Space-time analytic smoothing effect for the pseudo-conformally invariant Schrödinger equations

Gaku Hoshino, Tohru Ozawa

School of Advanced Science and Engineering

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

4 Citations (Scopus)

Abstract

We study the global Cauchy problem for the mass critical nonlinear Schrödinger equations. We prove the global existence of analytic solutions in both space and time variables for sufficiently small and exponentially decaying Cauchy data. The method of proof depends on the Leibniz rule for the generator of pseudo-conformal transforms at the L² critical level.

Original language	English
Article number	3
Pages (from-to)	1-10
Number of pages	10
Journal	Nonlinear Differential Equations and Applications
Volume	23
Issue number	1
DOIs	https://doi.org/10.1007/s00030-016-0362-5
Publication status	Published - 2016 Feb 1

Keywords

Analytic smoothing effect
Global existence
Nonlinear Schrödinger equation

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1007/s00030-016-0362-5

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title = "Space-time analytic smoothing effect for the pseudo-conformally invariant Schr{\"o}dinger equations",

abstract = "We study the global Cauchy problem for the mass critical nonlinear Schr{\"o}dinger equations. We prove the global existence of analytic solutions in both space and time variables for sufficiently small and exponentially decaying Cauchy data. The method of proof depends on the Leibniz rule for the generator of pseudo-conformal transforms at the L2 critical level.",

keywords = "Analytic smoothing effect, Global existence, Nonlinear Schr{\"o}dinger equation",

author = "Gaku Hoshino and Tohru Ozawa",

note = "Funding Information: This work was supported by Grant-in-Aid for JSPS Fellows.",

year = "2016",

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AU - Hoshino, Gaku

AU - Ozawa, Tohru

N1 - Funding Information: This work was supported by Grant-in-Aid for JSPS Fellows.

PY - 2016/2/1

Y1 - 2016/2/1

N2 - We study the global Cauchy problem for the mass critical nonlinear Schrödinger equations. We prove the global existence of analytic solutions in both space and time variables for sufficiently small and exponentially decaying Cauchy data. The method of proof depends on the Leibniz rule for the generator of pseudo-conformal transforms at the L2 critical level.

AB - We study the global Cauchy problem for the mass critical nonlinear Schrödinger equations. We prove the global existence of analytic solutions in both space and time variables for sufficiently small and exponentially decaying Cauchy data. The method of proof depends on the Leibniz rule for the generator of pseudo-conformal transforms at the L2 critical level.

KW - Analytic smoothing effect

KW - Global existence

KW - Nonlinear Schrödinger equation

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