Small data scattering of 2d Hartree type Dirac equations

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:506

Article

Cho, Yonggeun^1,2  Lee, Kiyeon³  Ozawa, Tohru⁴ 

[1] Jeonbuk Natl Univ, Dept Math, Jeonju 54896, South Korea

[2] Jeonbuk Natl Univ, Inst Pure & Appl Math, Jeonju 54896, South Korea

[3] Ewha Womans Univ, Dept Math, Seoul 03760, South Korea

[4] Waseda Univ, Dept Appl Phys, Shinjuku Ku, 3-4-1,Okubo, Tokyo 1698555, Japan

关键词: Dirac equations;    Coulomb type potential;    Global well-posedness;    Small data scattering;    Nonexistence of scattering;   

DOI  :  10.1016/j.jmaa.2021.125549

来源: Elsevier

【 摘 要 】

In this paper, we study the Cauchy problem of 2d Dirac equation with Hartree type nonlinearity c(vertical bar.vertical bar(-gamma)* )beta psi with c is an element of R \{0}, 0 < gamma < 2. Our aim is to show the small data global well-posedness and scattering in H-s for s > gamma - 1and 1 < gamma < 2. The difficulty stems from the singularity of the low-frequency part vertical bar xi vertical bar(-(2-gamma))chi({vertical bar xi vertical bar <= 1}) of potential. To overcome it we adapt U-p-V-p 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 < gamma <= 1. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

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