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arXiv · 2205.12000

Global Behavior of Small Data Solutions for The 2D Dirac-Klein-Gordon Equations

Shijie Dong·Kuijie Li·Yue Ma·Xu Yuan
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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 behaviors 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 imply 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, in particular, there is no restriction on the support of the initial data.

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Shijie Dong, Kuijie Li, Yue Ma, Xu Yuan. 2022-05-24. Global Behavior of Small Data Solutions for The 2D Dirac-Klein-Gordon Equations. https://arxiv.org/abs/2205.12000

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