On the global wellposedness for the nonlinear Schrödinger equations with Lp-large initial data

Ryosuke Hyakuna, Masayoshi Tsutsumi

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    4 Citations (Scopus)

    Abstract

    We consider the Cauchy problem for the nonlinear Schrödinger equations iut + u ± {pipe}u{pipe}p-1u=0, x ε ℝd, t ε ℝ u(x,0) = c0(x), x ε ℝd for 1 < p < 1 + 4/d and prove that there is a ρ(p,d) ε (1,2) such that the initial value problem is globally well posed for u0 ε Lρ with ρ(p, d) < ρ < 2.

    Original languageEnglish
    Pages (from-to)309-327
    Number of pages19
    JournalNonlinear Differential Equations and Applications
    Volume18
    Issue number3
    DOIs
    Publication statusPublished - 2011 Jun

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    Keywords

    • Cauchy problem
    • global solution
    • Large inital data
    • Nonlinear Schrödinger equation

    ASJC Scopus subject areas

    • Applied Mathematics
    • Analysis

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