On small data scattering of Hartree equations with short-range interaction

Yonggeun Cho, Gyeongha Hwang, Tohru Ozawa

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)

Abstract

In this note we study Hartree type equations with |∇| α (1 < α ≤ 2) and potential whose Fourier transform behaves like |ξ| - (d- γ1) at the origin and |ξ| - (d- γ2) at infinity. We show non-existence of scattering when 0 < 1 γ ≤ 1 and small data scattering in Hs for s > 2-α/2 when 2 < γ1 ≤ d and 0 < γ2 ≤ 2. For this we use Up - Vp space argument and Strichartz estimate.

Original languageEnglish
Pages (from-to)1809-1823
Number of pages15
JournalCommunications on Pure and Applied Analysis
Volume15
Issue number5
DOIs
Publication statusPublished - 2016 Sep

Keywords

  • Hartree equations
  • Short range potential
  • Small data scattering
  • Up and V p spaces

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Fingerprint

Dive into the research topics of 'On small data scattering of Hartree equations with short-range interaction'. Together they form a unique fingerprint.

Cite this