On Hartree equations with derivatives

Yonggeun Cho, Sanghyuk Lee, Tohru Ozawa

Research output: Contribution to journalArticlepeer-review

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

Keywords

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

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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