Global existence for the quadratic Dirac equation in two and three space dimensions

被引:1
作者
Zhang, Qian [1 ]
机构
[1] Beijing Normal Univ, Sch Math Sci, Lab Math & Complex Syst, Minist Educ, Beijing 100875, Peoples R China
关键词
Quadratic Dirac equation; Global-in-time solution; Sharp pointwise decay; Hyperboloidal foliation of spacetime; KLEIN-GORDON EQUATIONS; FIELD;
D O I
10.1016/j.jde.2022.11.015
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this paper we study global existence and pointwise decay estimates for the nonlinear Dirac equation with quadratic nonlinearity. We consider four cases depending on the spatial dimension n, the mass parameter m, and the initial data.0: i)(n, m) =(2, 0) and psi(0) is compactly supported; ii)(n, m) =(3, 0) and psi(0) is compactly supported; iii)(n, m) =(3, 0) and.0is not necessarily compactly supported; iv) n = 3, m >= 0 and psi(0) is compactly supported. In each of the cases i)-iii), we prove a small data global existence result, a sharp pointwise decay estimate and a scattering result for the global solution. In the case iv) we prove a uniform (in the mass parameter m) global existence result, a unified pointwise decay estimate, and a scattering result. (c) 2022 Elsevier Inc. All rights reserved.
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页码:696 / 734
页数:39
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