Nonlinear Schrödinger Equations in the Sobolev Space of Critical Order

M. Nakamura, T. Ozawa

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Abstract

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.

Original languageEnglish
Pages (from-to)364-380
Number of pages17
JournalJournal of Functional Analysis
Volume155
Issue number2
DOIs
Publication statusPublished - 1998 Jun 1

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ASJC Scopus subject areas

  • Analysis

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