二维和三维空间中狄拉克-克莱因-戈登系统的全局稳定性

IF 2.1 2区数学 Q1 MATHEMATICS

Calculus of Variations and Partial Differential Equations Pub Date : 2024-08-05 DOI:10.1007/s00526-024-02803-8

Qian Zhang

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引用次数: 0

摘要

在本文中，我们研究了二维和三维空间的狄拉克-克莱因-戈登（Dirac-Klein-Gordon）系统在小初始数据和规则初始数据下的全局非线性稳定性。在二维空间中，我们考虑了具有无质量狄拉克场和大质量标量场的狄拉克-克莱因-戈登系统，并证明了解的全局存在性、尖锐时间衰减估计和线性散射。在三维空间的情况下，我们考虑了在狄拉克方程中含有质量参数的狄拉克-克莱因-戈登系统，并证明了统一（质量参数）的全局存在性、统一的时间衰减估计和顶阶能量空间中的线性散射。

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Global stability of the Dirac–Klein–Gordon system in two and three space dimensions

In this paper we study global nonlinear stability for the Dirac–Klein–Gordon system in two and three space dimensions for small and regular initial data. In the case of two space dimensions, we consider the Dirac–Klein–Gordon system with a massless Dirac field and a massive scalar field, and prove global existence, sharp time decay estimates and linear scattering for the solutions. In the case of three space dimensions, we consider the Dirac–Klein–Gordon system with a mass parameter in the Dirac equation, and prove uniform (in the mass parameter) global existence, unified time decay estimates and linear scattering in the top order energy space.

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来源期刊

Calculus of Variations and Partial Differential Equations 数学-数学

CiteScore

3.30

自引率

4.80%

发文量

224

审稿时长

6 months

期刊介绍： Calculus of variations and partial differential equations are classical, very active, closely related areas of mathematics, with important ramifications in differential geometry and mathematical physics. In the last four decades this subject has enjoyed a flourishing development worldwide, which is still continuing and extending to broader perspectives. This journal will attract and collect many of the important top-quality contributions to this field of research, and stress the interactions between analysts, geometers, and physicists. The field of Calculus of Variations and Partial Differential Equations is extensive; nonetheless, the journal will be open to all interesting new developments. Topics to be covered include: - Minimization problems for variational integrals, existence and regularity theory for minimizers and critical points, geometric measure theory - Variational methods for partial differential equations, optimal mass transportation, linear and nonlinear eigenvalue problems - Variational problems in differential and complex geometry - Variational methods in global analysis and topology - Dynamical systems, symplectic geometry, periodic solutions of Hamiltonian systems - Variational methods in mathematical physics, nonlinear elasticity, asymptotic variational problems, homogenization, capillarity phenomena, free boundary problems and phase transitions - Monge-Ampère equations and other fully nonlinear partial differential equations related to problems in differential geometry, complex geometry, and physics.