Small data scattering of 2d Hartree type Dirac equations

Yonggeun Cho, Kiyeon Lee*, Tohru Ozawa

*この研究の対応する著者

研究成果: Article査読

抄録

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.

本文言語English
論文番号125549
ジャーナルJournal of Mathematical Analysis and Applications
506
1
DOI
出版ステータスPublished - 2022 2 1

ASJC Scopus subject areas

  • 分析
  • 応用数学

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