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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

We prove a sharp bilinear inequality for the Klein-Gordon equation on $\sr^{d+1}$, for any $d \geq 2$. This extends work of Ozawa-Rogers and Quilodr\'an for the Klein-Gordon equation and generalises work of Bez-Rogers for the wave equation.…

Analysis of PDEs · Mathematics 2013-02-22 Chris Jeavons

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

Considered herein is a particular nonlinear dispersive stochastic system consisting of Dirac and Klein-Gordon equations. They are coupled by nonlinear terms due to the Yukawa interaction. We consider a case of homogeneous multiplicative…

Analysis of PDEs · Mathematics 2024-05-29 Evgueni Dinvay , Sigmund Selberg

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

The Cauchy problem for a coupled Schroedinger and Benjamin - Ono system is shown to be globally well-posed for a class of data without finite energy. The proof uses the I-method introduced by Colliander, Keel, Staffilani, Takaoka, and Tao.

Analysis of PDEs · Mathematics 2007-05-23 Hartmut Pecher

We consider a class of wave-Schroedinger systems with a Zakharov-Schulman type coupling. This class of systems is indexed by a parameter gamma which measures the strength of the null form in the nonlinearity of the wave equation. The case…

Analysis of PDEs · Mathematics 2015-08-25 Thomas Beck , Fabio Pusateri , Philippe Sosoe , Percy Wong

We prove small data global existence and scattering for quasilinear systems of Klein-Gordon equations with different speeds, in dimension three. As an application, we obtain a robust global stability result for the Euler-Maxwell equations…

Analysis of PDEs · Mathematics 2012-08-14 Alexandru D. Ionescu , Benoit Pausader

In this article one will discuss the system of coupled nonlinear Klein-Gordon equations with different velocities and different masses. The nonlinearity considered is a general quadratic nonlinearity without any restriction. The method is a…

Analysis of PDEs · Mathematics 2011-11-21 Yue Ma

In this paper we are interested in the global well-posedness of the 3D Klein-Gordon-Zakharov equations with small initial data. We show the uniform boundedness of the energy for the global solution without any compactness assumptions on the…

Analysis of PDEs · Mathematics 2023-04-11 Xinyu Cheng , Jiao Xu

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 global well-posedness and scattering for the 3D Klein-Gordon-Schr\"odinger system for small radial data in the best known global well-posedness range $(u_0, n_0, n_1)\in L^2\times H^{ -\frac{1}{2} + \epsilon } \times…

Analysis of PDEs · Mathematics 2026-04-14 Vitor Borges , Tiklung Chan

In this paper we establish an almost optimal well-posedness and regularity theory for the Klein-Gordon-Schr\"odinger system on the half line. In particular we prove local-in-time well-posedness for rough initial data in Sobolev spaces of…

Analysis of PDEs · Mathematics 2018-03-15 E. Compaan , N. Tzirakis

We study the initial-boundary value problem for the coupled Klein-Gordon-Schr\"{o}dinger equations in a domain in $\mathbb R^N$ with $N \leq 4$. Under natural assumptions on the initial data, we prove the existence and uniqueness of global…

Analysis of PDEs · Mathematics 2022-12-19 Tohru Ozawa , Kenta Tomioka

In the present paper, we show that the global solution to (partially) damped Klein-Gordon equation on the three dimensional Euclidean space with small data decays exponentially. The key ingredients in the proof are: Morawetz-type estimates…

Analysis of PDEs · Mathematics 2024-12-10 Yan Cui , Bo Xia

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 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 consider a coupled Wave-Klein-Gordon system in 3D, and prove global regularity and modified scattering for small and smooth initial data with suitable decay at infinity. This system was derived by Wang and LeFloch-Ma as a simplified…

Analysis of PDEs · Mathematics 2019-11-26 Alexandru D. Ionescu , Benoit Pausader

This paper studies the regularity of solutions to the Zakharov and Klein-Gordon-Schr\"{o}dinger systems at low regularity levels. The main result is that the nonlinear part of the solution flow falls in a smoother space than the initial…

Analysis of PDEs · Mathematics 2016-05-19 E. Compaan

We prove global wellposedness of the Klein-Gordon equation with power nonlinearity $|u|^{\alpha-1}u$, where $\alpha\in\left[1,\frac{d}{d-2}\right]$, in dimension $d\geq3$ with initial data in $M_{p, p'}^{1}(\mathbb{R}^d)\times…

Analysis of PDEs · Mathematics 2021-08-10 Leonid Chaichenets , Nikolaos Pattakos