On the cauchy problem of fractional schrödinger equation with hartree type nonlinearity

Yonggeun Cho, Hichem Hajaiej, Gyeongha Hwang, Tohru Ozawa

    Research output: Contribution to journalArticle

    50 Citations (Scopus)

    Abstract

    We study the Cauchy problem for the fractional Schrodinger equation iδtu = (m2 -Δ) α/2u + F(u) in R1+n, where n ≥1, m ≥ 0, 1 < α < 2, and F stands for the nonlinearity of Hartree type F(u)-λ(ψ(.)|•|*|u|2)u with λ= ±1, 0 < γ < n, and 0 ≤ ψ ∈ L(Rn). We prove the existence and uniqueness of local and global solutions for certain α, γ, λ, ψ. We also remark on finite time blowup of solutions when λ =-1.

    Original languageEnglish
    Pages (from-to)193-224
    Number of pages32
    JournalFunkcialaj Ekvacioj
    Volume56
    Issue number2
    DOIs
    Publication statusPublished - 2013 Aug 26

    Fingerprint

    Finite Time Blow-up
    Schrodinger Equation
    Blow-up of Solutions
    Local Solution
    Global Solution
    Cauchy Problem
    Existence and Uniqueness
    Fractional
    Nonlinearity

    Keywords

    • Finite time blowup
    • Fractional schrödinger equation
    • Hartree type nonlinearity
    • Strichartz estimates

    ASJC Scopus subject areas

    • Algebra and Number Theory
    • Analysis
    • Geometry and Topology

    Cite this

    On the cauchy problem of fractional schrödinger equation with hartree type nonlinearity. / Cho, Yonggeun; Hajaiej, Hichem; Hwang, Gyeongha; Ozawa, Tohru.

    In: Funkcialaj Ekvacioj, Vol. 56, No. 2, 26.08.2013, p. 193-224.

    Research output: Contribution to journalArticle

    Cho, Yonggeun ; Hajaiej, Hichem ; Hwang, Gyeongha ; Ozawa, Tohru. / On the cauchy problem of fractional schrödinger equation with hartree type nonlinearity. In: Funkcialaj Ekvacioj. 2013 ; Vol. 56, No. 2. pp. 193-224.
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