Nonlinear Schrödinger Equations in the Sobolev Space of Critical Order

M. Nakamura; T. Ozawa

doi:10.1006/jfan.1997.3236

Nonlinear Schrödinger Equations in the Sobolev Space of Critical Order

M. Nakamura^*, T. Ozawa

^*Corresponding author for this work

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

81 Citations (Scopus)

Abstract

The Cauchy problem for the nonlinear Schrödinger equations is considered in the Sobolev spaceH^n/2(Rⁿ) of critical ordern/2, where the embedding intoL^∞(Rⁿ) breaks down and any power behavior of interaction works as a subcritical nonlinearity. Under the interaction of exponential type the existence and uniqueness is proved for globalH^n/2-solutions with small Cauchy data.

Original language	English
Pages (from-to)	364-380
Number of pages	17
Journal	Journal of Functional Analysis
Volume	155
Issue number	2
DOIs	https://doi.org/10.1006/jfan.1997.3236
Publication status	Published - 1998 Jun 1
Externally published	Yes

ASJC Scopus subject areas

Analysis

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title = "Nonlinear Schr{\"o}dinger Equations in the Sobolev Space of Critical Order",

abstract = "The Cauchy problem for the nonlinear Schr{\"o}dinger equations is considered in the Sobolev spaceHn/2(Rn) of critical ordern/2, where the embedding intoL∞(Rn) breaks down and any power behavior of interaction works as a subcritical nonlinearity. Under the interaction of exponential type the existence and uniqueness is proved for globalHn/2-solutions with small Cauchy data.",

author = "M. Nakamura and T. Ozawa",

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N2 - The Cauchy problem for the nonlinear Schrödinger equations is considered in the Sobolev spaceHn/2(Rn) of critical ordern/2, where the embedding intoL∞(Rn) breaks down and any power behavior of interaction works as a subcritical nonlinearity. Under the interaction of exponential type the existence and uniqueness is proved for globalHn/2-solutions with small Cauchy data.

AB - The Cauchy problem for the nonlinear Schrödinger equations is considered in the Sobolev spaceHn/2(Rn) of critical ordern/2, where the embedding intoL∞(Rn) breaks down and any power behavior of interaction works as a subcritical nonlinearity. Under the interaction of exponential type the existence and uniqueness is proved for globalHn/2-solutions with small Cauchy data.

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DO - 10.1006/jfan.1997.3236

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Nonlinear Schrödinger Equations in the Sobolev Space of Critical Order

Abstract

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