On radial solutions of semi-relativistic Hartree equations

Yonggeun Cho, Tohru Ozawa

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

We consider the semi-relativistic Hartree type equation with nonlocal nonlinearity F(u) = λ(|x| * |u| 2)u,0 < γ < n,n ≥ 1. In [2, 3], the global well-posedness (GWP) was shown for the value of γ ∈ (0, 2n/n+1),n ≥ 2 with large data and γ ∈ (2, n), n ≥ 3 with small data. In this paper" we extend the previous GWP result to the case for γ ∈ (1, 2n-1/n),n ≥ 2 with radially symmetric large data. Solutions in a weighted Sobolev space are also studied.

Original languageEnglish
Pages (from-to)71-82
Number of pages12
JournalDiscrete and Continuous Dynamical Systems - Series S
Volume1
Issue number1
DOIs
Publication statusPublished - 2008 Mar 1
Externally publishedYes

Keywords

  • Global well-posedness
  • Radially symmetric solution
  • Semi-relativistic Hartree type equation

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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