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

51 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

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Keywords

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

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

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