Scattering theory for the Hartree equation

Nakao Hayashi, Pavel I. Naumkin, Tohru Ozawa

Research output: Contribution to journalArticle

25 Citations (Scopus)

Abstract

We study the scattering problem for the Hartree equation i∂tu = - 1/2Δu +f(\u\2)u, (t,x) ∈ R x Rn, with initial data u(0,x) = U0(X), x ∈ Rn, where f(|u|2) = V * |u|2, V(x) = λ|x|-1, λ ∈ R, n ≥ 2. We prove that for any U0 ∈ H0,γ∩ Hγ,0, with 1/2 < γ < n/2, such that the value ∈ = ∥u0∥0,γ + ∥u0∥γ,0 is sufficiently small, there exist unique u± 6 H'0 n /f0''7 with

Original languageEnglish
Pages (from-to)1256-1267
Number of pages12
JournalSIAM Journal on Mathematical Analysis
Volume29
Issue number5
DOIs
Publication statusPublished - 1998 Sep

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Keywords

  • Asymptotic behavior
  • Hartree equation
  • Scattering

ASJC Scopus subject areas

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

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