Global behavior of small data solutions for the 2D Dirac-Klein-Gordon system

IF 1.2 2区数学 Q1 MATHEMATICS

Transactions of the American Mathematical Society Pub Date : 2023-10-11 DOI:10.1090/tran/9011

Shijie Dong, Kuijie Li, Yue Ma, Xu Yuan

引用次数: 0

Abstract

In this paper, we are interested in the two-dimensional Dirac–Klein-Gordon system, which is a basic model in particle physics. We investigate the global behavior of small data solutions to this system in the case of a massive scalar field and a massless Dirac field. More precisely, our main result is twofold: (1) we show sharp time decay for the pointwise estimates of the solutions, which implies the asymptotic stability of this system; (2) we show the linear scattering result of this system which is a fundamental problem when it is viewed as dispersive equations. Our result is valid for general small, high-regular initial data, and in particular, there is no restriction on the support of the initial data.

查看原文本刊更多论文

二维Dirac-Klein-Gordon系统小数据解的全局行为

本文主要研究二维Dirac-Klein-Gordon系统，这是粒子物理学中的一个基本模型。我们研究了该系统在大质量标量场和无质量狄拉克场情况下的小数据解的全局行为。更准确地说，我们的主要结果是双重的:(1)我们显示了解的点估计的明显时间衰减，这意味着该系统的渐近稳定性;(2)给出了该系统的线性散射结果，这是将其看作色散方程时的一个基本问题。我们的结果对于一般的小的、高规则的初始数据是有效的，特别是对初始数据的支持度没有限制。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Transactions of the American Mathematical Society 数学-数学

CiteScore

2.30

自引率

7.70%

发文量

171

审稿时长

3-6 weeks

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to research articles in all areas of pure and applied mathematics. To be published in the Transactions, a paper must be correct, new, and significant. Further, it must be well written and of interest to a substantial number of mathematicians. Piecemeal results, such as an inconclusive step toward an unproved major theorem or a minor variation on a known result, are in general not acceptable for publication. Papers of less than 15 printed pages that meet the above criteria should be submitted to the Proceedings of the American Mathematical Society. Published pages are the same size as those generated in the style files provided for AMS-LaTeX.