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Volume 14
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Article

Global Behavior of the 2D Dirac–Klein–Gordon System with a Class of Large Initial Data

by
Qian Zhang
School of Mathematical Sciences, Tiangong University, Tianjin 300387, China
Mathematics 2026, 14(10), 1718; https://doi.org/10.3390/math14101718 (registering DOI)
Submission received: 28 March 2026 / Revised: 12 May 2026 / Accepted: 13 May 2026 / Published: 16 May 2026
(This article belongs to the Section C1: Difference and Differential Equations)
Versions Notes

Abstract

In this paper, we derive the global dynamic properties of the Dirac–Klein–Gordon system in R1+2 with a class of large initial data. We consider the case of a massless Dirac field coupled with a massive Klein–Gordon field. The initial data are bounded in certain weighted Sobolev spaces, where the Dirac field is small while the Klein–Gordon field can be arbitrarily large. We establish global existence and characterize the asymptotic behavior of the solutions, including sharp time decay and linear scattering.
Keywords: Dirac–Klein–Gordon system; large initial data; global existence theory; pointwise decay estimates; linear scattering theory Dirac–Klein–Gordon system; large initial data; global existence theory; pointwise decay estimates; linear scattering theory

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MDPI and ACS Style

Zhang, Q. Global Behavior of the 2D Dirac–Klein–Gordon System with a Class of Large Initial Data. Mathematics 2026, 14, 1718. https://doi.org/10.3390/math14101718

AMA Style

Zhang Q. Global Behavior of the 2D Dirac–Klein–Gordon System with a Class of Large Initial Data. Mathematics. 2026; 14(10):1718. https://doi.org/10.3390/math14101718

Chicago/Turabian Style

Zhang, Qian. 2026. "Global Behavior of the 2D Dirac–Klein–Gordon System with a Class of Large Initial Data" Mathematics 14, no. 10: 1718. https://doi.org/10.3390/math14101718

APA Style

Zhang, Q. (2026). Global Behavior of the 2D Dirac–Klein–Gordon System with a Class of Large Initial Data. Mathematics, 14(10), 1718. https://doi.org/10.3390/math14101718

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