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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

From the work on the weak-null condition by Lindblad and Rodnianski, it is well-known that `bad' quadratic sourcing terms are allowed to appear in coupled semilinear wave equations in three spatial dimensions, provided that such terms…

Analysis of PDEs · Mathematics 2022-08-15 Shijie Dong , Zoe Wyatt

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

We are interested in studying the coupled wave and Klein-Gordon equations with null quadratic nonlinearities in $\mathbb{R}^{2+1}$. We want to establish the small data global existence result, and in addition, we also demonstrate the…

Analysis of PDEs · Mathematics 2020-05-12 Shijie Dong

We consider the coupled systems of nonlinear wave and Klein-Gordon equations in two space dimensions with cubic nonlinearity. For this kind of systems, the small data global existence is already known if the cubic nonlinearity satisfies a…

Analysis of PDEs · Mathematics 2022-05-30 Minggang Cheng

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

In this work we consider the problem of global existence of small regular solutions to a type nonlinear wave-Klein-Gordon system with semi-linear interactions in two spatial dimension. We develop some new techniques on both wave equations…

Analysis of PDEs · Mathematics 2017-12-15 Yue MA

We prove almost global well-posedness for quasilinear strongly coupled wave-Klein-Gordon systems with small and localized data in two space dimensions. We assume only mild decay on the data at infinity as well as minimal regularity. We…

Analysis of PDEs · Mathematics 2025-08-13 Mihaela Ifrim , Annalaura Stingo

We are interested in coupled semi-linear wave equations satisfying the null condition in two space dimensions, a basic model in nonlinear wave equations. Our aim is to establish global existence of smooth solutions to this system with large…

Analysis of PDEs · Mathematics 2025-07-21 Bingbing Ding , Shijie Dong , Gang Xu

In this paper we prove global existence and global behavior of solutions to quasilinear wave-Klein-Gordon systems in $\mathbb{R}^{1+2}$ with quadratic nonlinearities satisfying the null condition. We consider small, regular and compactly…

Analysis of PDEs · Mathematics 2023-12-07 Qian Zhang

We are interested in establishing stability results for a system of semilinear wave and Klein-Gordon equations with mixed coupling nonlinearities, that is, we consider all of the possible quadratic nonlinear terms of the type of wave and…

Analysis of PDEs · Mathematics 2020-07-17 Shijie Dong

We consider the Cauchy problem for quadratic nonlinear Klein-Gordon systems in two space dimensions with masses satisfying the resonance relation. Under the null condition in the sense of J.-M. Delort, D. Fang, R. Xue (2004), we show the…

Analysis of PDEs · Mathematics 2011-05-11 Soichiro Katayama , Tohru Ozawa , Hideaki Sunagawa

We consider a coupled Wave-Klein-Gordon system in 3D, which is a simplified model for the global nonlinear stability of the Minkowski space-time for self-gravitating massive fields. In this paper we study the large-time asymptotic behavior…

Analysis of PDEs · Mathematics 2023-04-12 Zhimeng Ouyang

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

In this article we will prove the global existence of a type of wave-Klein-Gordon system in $2+1$ spacetime dimension. Some technical tools such as conformal energy estimate on hyperboloid, normal form transform on Klein-Gordon equations…

Analysis of PDEs · Mathematics 2019-07-09 Yue Ma

We consider the Cauchy problem for coupled systems of wave and Klein-Gordon equations with quadratic nonlinearity in three space dimensions. We show global existence of small amplitude solutions under certain condition including the null…

Analysis of PDEs · Mathematics 2012-01-17 Soichiro Katayama

We are interested in the Klein-Gordon-Zakharov system in $\mathbb{R}^{1+2}$, which is an important model in plasma physics with extensive mathematical studies. The system can be regarded as semilinear coupled wave and Klein-Gordon equations…

Analysis of PDEs · Mathematics 2021-11-02 Shijie Dong , Yue Ma

We describe completely 2-solitary waves related to the ground state of the nonlinear damped Klein-Gordon equation \begin{equation*} \partial_{tt}u+2\alpha\partial_{t}u-\Delta u+u-|u|^{p-1}u=0 \end{equation*} on $\bf R^N$, for $1\leq N\leq…

Analysis of PDEs · Mathematics 2019-08-27 Raphaël Côte , Yvan Martel , Xu Yuan , Lifeng Zhao

We study in $\mathbb{R}^{3+1}$ a system of nonlinearly coupled Klein-Gordon equations under null condition, with (possibly vanishing) mass varying in the interval $[0, 1]$. Our goal is three folds: 1) we want to establish the global…

Analysis of PDEs · Mathematics 2020-04-23 Shijie Dong

In this article we will develop some techniques aimed at the strong couplings in two-dimensional wave-Klein-Gordon system. We distinguish the roles of different type of decay factors and develop a method which permits us to "exchange" one…

Analysis of PDEs · Mathematics 2021-04-02 Yue Ma
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