On small data scattering of Hartree equations with short-range interaction

Yonggeun Cho, Gyeongha Hwang, Tohru Ozawa

    研究成果: Article

    5 引用 (Scopus)

    抄録

    In this note we study Hartree type equations with |∇| α (1 <α ≤ 2) and potential whose Fourier transform behaves like |ξ| - (d- γ1) at the origin and |ξ| - (d- γ2) at infinity. We show non-existence of scattering when 0 <1 γ ≤ 1 and small data scattering in Hs for s > 2-α/2 when 2 <γ1 ≤ d and 0 <γ2 ≤ 2. For this we use Up - Vp space argument and Strichartz estimate.

    元の言語English
    ページ(範囲)1809-1823
    ページ数15
    ジャーナルCommunications on Pure and Applied Analysis
    15
    発行部数5
    DOI
    出版物ステータスPublished - 2016 9 1

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    Hartree Equation
    Strichartz Estimates
    Scattering
    Interaction
    Range of data

    ASJC Scopus subject areas

    • Analysis
    • Applied Mathematics

    これを引用

    On small data scattering of Hartree equations with short-range interaction. / Cho, Yonggeun; Hwang, Gyeongha; Ozawa, Tohru.

    :: Communications on Pure and Applied Analysis, 巻 15, 番号 5, 01.09.2016, p. 1809-1823.

    研究成果: Article

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    AB - In this note we study Hartree type equations with |∇| α (1 <α ≤ 2) and potential whose Fourier transform behaves like |ξ| - (d- γ1) at the origin and |ξ| - (d- γ2) at infinity. We show non-existence of scattering when 0 <1 γ ≤ 1 and small data scattering in Hs for s > 2-α/2 when 2 <γ1 ≤ d and 0 <γ2 ≤ 2. For this we use Up - Vp space argument and Strichartz estimate.

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