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

Yonggeun Cho, Gyeongha Hwang, Tohru Ozawa

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    5 Citations (Scopus)

    Abstract

    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.

    Original languageEnglish
    Pages (from-to)1809-1823
    Number of pages15
    JournalCommunications on Pure and Applied Analysis
    Volume15
    Issue number5
    DOIs
    Publication statusPublished - 2016 Sep 1

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    Keywords

    • Hartree equations
    • Short range potential
    • Small data scattering
    • Up and V p spaces

    ASJC Scopus subject areas

    • Analysis
    • Applied Mathematics

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