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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…

Analysis of PDEs · Mathematics 2023-03-16 Qian Zhang

We study the Dirac--Klein-Gordon system in $1+2$ spacetime dimensions. We show global existence of the solutions, as well as sharp time decay and linear scattering. One key advance is that we provide the first asymptotic stability result…

Analysis of PDEs · Mathematics 2023-11-15 Shijie Dong , Zoe Wyatt

We obtain conditional results on the global existence and scattering for large solutions of the Dirac-Klein-Gordon system in critical spaces in dimension $1+3$. In particular, for bounded solutions we identify a space-time Lebesgue norm…

Analysis of PDEs · Mathematics 2018-06-25 Timothy Candy , Sebastian Herr

We are interested in four-dimensional Dirac-Klein-Gordon equations, a fundamental model in particle physics. The main goal of this paper is to establish global existence of solutions to the coupled system and to explore their long-time…

Analysis of PDEs · Mathematics 2024-07-09 Jingya Zhao

The aim of this paper is to study the global existence of solutions to a coupled wave-Klein-Gordon system in space dimension two when initial data are small, smooth and mildly decaying at infinity. Some physical models strictly related to…

Analysis of PDEs · Mathematics 2018-10-25 Annalaura Stingo

In this paper we are interested in the coupled wave and Klein-Gordon equations in $\mathbb{R}^+\times\mathbb{R}^2$. We want to establish the global well-posedness of such system by showing the uniform boundedness of the energy for the…

Analysis of PDEs · Mathematics 2023-12-06 Xinyu Cheng

We are interested in the cubic Dirac equation in two space dimensions. We establish the small data global existence and sharp pointwise decay results for general cubic nonlinearities without additional structure. We also prove the…

Analysis of PDEs · Mathematics 2023-03-14 Qian Zhang

We study the Klein-Gordon-Zakharov system in two spatial dimensions, an important model in plasma physics. For small, smooth, and spatially localized initial data, we establish the global existence of solutions and characterize their sharp…

Analysis of PDEs · Mathematics 2025-09-04 Shijie Dong , Zihua Guo , Kuijie Li

We investigate the long-time behavior of solutions with small initial data to the viscoelastic Klein-Gordon equation with general smooth nonlinearity. Our analysis relies on the space-time resonances method to eliminate all nonresonant…

Analysis of PDEs · Mathematics 2026-03-04 Louis Garénaux , Björn de Rijk

We consider the massive Dirac-Klein-Gordon system in two space dimensions. Under the non-resonace mass condition, we show that the solution is asymptotically free if the initial data are sufficiently small in a suitable weighted Sobolev…

Analysis of PDEs · Mathematics 2011-11-22 Masahiro Ikeda , Akihiro Shimomura , Hideaki Sunagawa

In this paper we study global nonlinear stability for a system of semilinear wave and Klein-Gordon equations with quadratic nonlinearities. We consider nonlinearities of the type of wave-Klein-Gordon interactions where there are no…

Analysis of PDEs · Mathematics 2023-03-14 Qian Zhang

We study the 2D coupled wave-Klein-Gordon systems with semi-linear null nonlinearities $Q_0$ and $Q_{\alpha\beta}$. The main result states that the solution to the 2D coupled systems exists globally provided that the initial data are small…

Analysis of PDEs · Mathematics 2022-02-17 Shijie Dong , Yue Ma , Xu Yuan

We consider the Dirac equation with cubic Hartree-type nonlinearity derived by uncoupling the Dirac-Klein-Gordon systems. We prove small data scattering result in full subcritical range. Main ingredients of the proof are the localized…

Analysis of PDEs · Mathematics 2018-06-20 Changhun Yang

We prove global well-posedness and scattering for the massive Dirac-Klein-Gordon system with small and low regularity initial data in dimension two. To achieve this, we impose a non-resonance condition on the masses.

Analysis of PDEs · Mathematics 2025-01-08 Ioan Bejenaru , Vitor Borges

The Cauchy problem for the classical Dirac-Klein-Gordon system in two space dimensions is globally well-posed for L^2 Schoedinger data and wave data in H^{1/2} \times H^{-1/2}. In the case of smooth data there exists a global smooth…

Analysis of PDEs · Mathematics 2009-06-22 Axel Gruenrock , Hartmut Pecher

Consider the Klein-Gordon-Zakharov equations in $\mathbb{R}^{1+2}$, and we are interested in establishing the small global solution to the equations and in investigating the pointwise asymptotic behavior of the solution. The…

Analysis of PDEs · Mathematics 2021-02-24 Shijie Dong

It is known that the Maxwell-Klein-Gordon equations in $\mathbb{R}^{3+1}$ admit global solutions with finite energy data. In this paper, we present a new approach to study the asymptotic behavior of these global solutions. We show the…

Analysis of PDEs · Mathematics 2015-11-03 Shiwu Yang

On the (1+3) dimensional Minkowski spacetime, for small, regular initial data, it is well-known that the Dirac-Klein-Gordon system admits a global solution. In the present paper, we aim to establish the uniform boundedness of the total…

Analysis of PDEs · Mathematics 2022-08-31 Shijie Dong , Kuijie Li , Xu Yuan

We consider general semilinear, multispeed Klein-Gordon systems in space dimension two with some non-degeneracy conditions. We prove that with small initial data such solutions are always global and scatter to a linear solution. This result…

Analysis of PDEs · Mathematics 2023-12-18 Xilu Zhu

We initiate the study of the asymptotic behavior of small solutions to one-dimensional Klein-Gordon equations with variable coefficient quadratic nonlinearities. The main discovery in this work is a striking resonant interaction between…

Analysis of PDEs · Mathematics 2021-06-16 Hans Lindblad , Jonas Luhrmann , Avy Soffer
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