On Hartree equations with derivatives

Yonggeun Cho, Sanghyuk Lee, Tohru Ozawa

    Research output: Contribution to journalArticle

    6 Citations (Scopus)

    Abstract

    We consider the Cauchy problem of two types of Hartree equations with exchangecorrelation correction terms: {iut - Δu = V k(u)u in ℝ1+n, k = 1,2,u(0) = φ in ℝn, n ≥ 1, where V1(u) = |x|*1|u|2 + λ2|∇u| 2),V2(u) = |x| *∥∇|δu|2). We establish the well-posedness of Cauchy problems and show the smoothing effect of solutions for each 0 < γ < n and 0 ≤ δ ≤ 1.

    Original languageEnglish
    Pages (from-to)2094-2108
    Number of pages15
    JournalNonlinear Analysis, Theory, Methods and Applications
    Volume74
    Issue number6
    DOIs
    Publication statusPublished - 2011 Mar 15

    Fingerprint

    Hartree Equation
    Cauchy Problem
    Derivatives
    Smoothing Effect
    Derivative
    Well-posedness
    Term

    Keywords

    • Angular regularity
    • Hartree equations with derivatives
    • Smoothing effect
    • Well-posedness

    ASJC Scopus subject areas

    • Analysis
    • Applied Mathematics

    Cite this

    On Hartree equations with derivatives. / Cho, Yonggeun; Lee, Sanghyuk; Ozawa, Tohru.

    In: Nonlinear Analysis, Theory, Methods and Applications, Vol. 74, No. 6, 15.03.2011, p. 2094-2108.

    Research output: Contribution to journalArticle

    Cho, Yonggeun ; Lee, Sanghyuk ; Ozawa, Tohru. / On Hartree equations with derivatives. In: Nonlinear Analysis, Theory, Methods and Applications. 2011 ; Vol. 74, No. 6. pp. 2094-2108.
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