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
Publication statusPublished - 1998 Sep
Externally publishedYes

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Hartree Equation
Scattering Theory
Scattering Problems
Scattering

Keywords

  • Asymptotic behavior
  • Hartree equation
  • Scattering

ASJC Scopus subject areas

  • Mathematics(all)
  • Analysis
  • Applied Mathematics

Cite this

Scattering theory for the Hartree equation. / Hayashi, Nakao; Naumkin, Pavel I.; Ozawa, Tohru.

In: SIAM Journal on Mathematical Analysis, Vol. 29, No. 5, 09.1998, p. 1256-1267.

Research output: Contribution to journalArticle

Hayashi, N, Naumkin, PI & Ozawa, T 1998, 'Scattering theory for the Hartree equation', SIAM Journal on Mathematical Analysis, vol. 29, no. 5, pp. 1256-1267.
Hayashi, Nakao ; Naumkin, Pavel I. ; Ozawa, Tohru. / Scattering theory for the Hartree equation. In: SIAM Journal on Mathematical Analysis. 1998 ; Vol. 29, No. 5. pp. 1256-1267.
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