Small data scattering of 2d Hartree type Dirac equations

Yonggeun Cho, Kiyeon Lee*, Tohru Ozawa

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we study the Cauchy problem of 2d Dirac equation with Hartree type nonlinearity c(|⋅|−γ⁎〈ψ,βψ〉)βψ with c∈R∖{0}, 0<γ<2. Our aim is to show the small data global well-posedness and scattering in Hs for s>γ−1 and 1<γ<2. The difficulty stems from the singularity of the low-frequency part |ξ|−(2−γ)χ{|ξ|≤1} of potential. To overcome it we adapt Up−Vp space argument and bilinear estimates of [27,25] arising from the null structure. We also provide nonexistence result for scattering in the long-range case 0<γ≤1.

Original languageEnglish
Article number125549
JournalJournal of Mathematical Analysis and Applications
Volume506
Issue number1
DOIs
Publication statusPublished - 2022 Feb 1

Keywords

  • Coulomb type potential
  • Dirac equations
  • Global well-posedness
  • Nonexistence of scattering
  • Small data scattering

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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