On the global well-posedness for the nonlinear Schrdinger equations with large initial data of infinite L2 norm

Ryosuke Hyakuna, Takamasa Tanaka, Masayoshi Tsutsumi

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    4 Citations (Scopus)

    Abstract

    It is shown that the Cauchy problem for the nonlinear Schrdinger equations iut+△u±|u|p-1u=0,x∈ℝd, t>0 is globally well-posed for a class of initial data which lie in a Lq space with q near 2 when 1<p<1+4d and d≤4.

    Original languageEnglish
    Pages (from-to)1304-1319
    Number of pages16
    JournalNonlinear Analysis, Theory, Methods and Applications
    Volume74
    Issue number4
    DOIs
    Publication statusPublished - 2011 Feb 15

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    Keywords

    • Cauchy problem
    • Global solution
    • Large initial data
    • Lp-initial data
    • Nonlinear Schrdinger equations

    ASJC Scopus subject areas

    • Analysis
    • Applied Mathematics

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