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

Ryosuke Hyakuna, Masayoshi Tsutsumi

    Research output: Contribution to journalArticle

    3 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

    Fingerprint

    Global Well-posedness
    Nonlinear equations
    Initial Value Problem
    Cauchy Problem
    Nonlinear Equations
    Pipe
    Initial value problems

    Keywords

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

    ASJC Scopus subject areas

    • Applied Mathematics
    • Analysis

    Cite this

    On the global wellposedness for the nonlinear Schrödinger equations with Lp-large initial data. / Hyakuna, Ryosuke; Tsutsumi, Masayoshi.

    In: Nonlinear Differential Equations and Applications, Vol. 18, No. 3, 06.2011, p. 309-327.

    Research output: Contribution to journalArticle

    @article{e5eec1b0f4094599995dd4f37b77ecc0,
    title = "On the global wellposedness for the nonlinear Schr{\"o}dinger equations with Lp-large initial data",
    abstract = "We consider the Cauchy problem for the nonlinear Schr{\"o}dinger 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.",
    keywords = "Cauchy problem, global solution, Large inital data, Nonlinear Schr{\"o}dinger equation",
    author = "Ryosuke Hyakuna and Masayoshi Tsutsumi",
    year = "2011",
    month = "6",
    doi = "10.1007/s00030-011-0097-2",
    language = "English",
    volume = "18",
    pages = "309--327",
    journal = "Nonlinear Differential Equations and Applications",
    issn = "1021-9722",
    publisher = "Birkhauser Verlag Basel",
    number = "3",

    }

    TY - JOUR

    T1 - On the global wellposedness for the nonlinear Schrödinger equations with Lp-large initial data

    AU - Hyakuna, Ryosuke

    AU - Tsutsumi, Masayoshi

    PY - 2011/6

    Y1 - 2011/6

    N2 - 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.

    AB - 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.

    KW - Cauchy problem

    KW - global solution

    KW - Large inital data

    KW - Nonlinear Schrödinger equation

    UR - http://www.scopus.com/inward/record.url?scp=79957537695&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=79957537695&partnerID=8YFLogxK

    U2 - 10.1007/s00030-011-0097-2

    DO - 10.1007/s00030-011-0097-2

    M3 - Article

    AN - SCOPUS:79957537695

    VL - 18

    SP - 309

    EP - 327

    JO - Nonlinear Differential Equations and Applications

    JF - Nonlinear Differential Equations and Applications

    SN - 1021-9722

    IS - 3

    ER -