Analytic smoothing effect for a system of Schrödinger equations with three wave interaction

Gaku Hoshino, Tohru Ozawa

    Research output: Contribution to journalArticle

    3 Citations (Scopus)

    Abstract

    We consider the global Cauchy problem for a system of Schrödinger equations with quadratic interaction. Two types of analytic smoothing effect for the solutions are formulated in the small data setting under the mass resonance condition. One is the usual analytic smoothing effect in space variables in terms of the generator of Galilei transforms. We prove the existence and uniqueness of global solutions which are analytic with respect to Galilei generators for sufficiently small data with exponential decay at infinity in space ℝn with n ≥ 3. The other is analytic smoothing effect in space-time variables in terms of generator of pseudo-conformal and Galilei transforms. We prove the existence and uniqueness of global solutions which are analytic with respect to pseudo-conformal and Galilei generators for sufficiently small data with exponential decay in ℝ4. We also discuss the associated Lagrange structure.

    Original languageEnglish
    Article number091513
    JournalJournal of Mathematical Physics
    Volume56
    Issue number9
    DOIs
    Publication statusPublished - 2015

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    Smoothing Effect
    Wave Interaction
    wave interaction
    smoothing
    System of equations
    generators
    Generator
    uniqueness
    Exponential Decay
    Global Solution
    Existence and Uniqueness
    Cauchy problem
    Transform
    decay
    infinity
    Lagrange
    Cauchy Problem
    Space-time
    Infinity
    Interaction

    ASJC Scopus subject areas

    • Statistical and Nonlinear Physics
    • Mathematical Physics

    Cite this

    Analytic smoothing effect for a system of Schrödinger equations with three wave interaction. / Hoshino, Gaku; Ozawa, Tohru.

    In: Journal of Mathematical Physics, Vol. 56, No. 9, 091513, 2015.

    Research output: Contribution to journalArticle

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