On existence of global solutions of schrödinger equations with subcritical nonlinearity for L{frown} p-initial data

Ryosuke Hyakuna, Masayoshi Tsutsumi

    Research output: Contribution to journal › Article

    10 Citations (Scopus)

    Abstract

    We construct a local theory of the Cauchy problem for the nonlinear Schrödinger equations with α ∈ (1, 5) and u 0 ∈ L{frown} p(ℝ) when p lies in an open neighborhood of 2. Moreover we prove the global existence for the initial value problem when p is sufficiently close to 2.

    Original languageEnglish
    Pages (from-to)3905-3920
    Number of pages16
    JournalProceedings of the American Mathematical Society
    Volume140
    Issue number11
    DOIs
    Publication statusPublished - 2012

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    Initial value problems
    Nonlinear equations
    Global Solution
    Global Existence
    Initial Value Problem
    Cauchy Problem
    Nonlinear Equations
    Nonlinearity

    ASJC Scopus subject areas

    • Mathematics(all)
    • Applied Mathematics

    Cite this

    On existence of global solutions of schrödinger equations with subcritical nonlinearity for L{frown} p-initial data. / Hyakuna, Ryosuke; Tsutsumi, Masayoshi.

    In: Proceedings of the American Mathematical Society, Vol. 140, No. 11, 2012, p. 3905-3920.

    Research output: Contribution to journal › Article

    Hyakuna, R & Tsutsumi, M 2012, 'On existence of global solutions of schrödinger equations with subcritical nonlinearity for L{frown} p-initial data', Proceedings of the American Mathematical Society, vol. 140, no. 11, pp. 3905-3920. https://doi.org/10.1090/S0002-9939-2012-11314-0
    Hyakuna R, Tsutsumi M. On existence of global solutions of schrödinger equations with subcritical nonlinearity for L{frown} p-initial data. Proceedings of the American Mathematical Society. 2012;140(11):3905-3920. https://doi.org/10.1090/S0002-9939-2012-11314-0
    Hyakuna, Ryosuke ; Tsutsumi, Masayoshi. / On existence of global solutions of schrödinger equations with subcritical nonlinearity for L{frown} p-initial data. In: Proceedings of the American Mathematical Society. 2012 ; Vol. 140, No. 11. pp. 3905-3920.
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