# On global dynamics of the Maxwell–Klein–Gordon equations

@article{Yang2019OnGD,
title={On global dynamics of the Maxwell–Klein–Gordon equations},
author={Shi-Zheng Yang and Pin Yu},
journal={Cambridge Journal of Mathematics},
year={2019}
}
• Published 30 March 2018
• Mathematics, Physics
• Cambridge Journal of Mathematics
On the three dimensional Euclidean space, for data with finite energy, it is well-known that the Maxwell-Klein-Gordon equations admit global solutions. However, the asymptotic behaviours of the solutions for the data with non-vanishing charge and arbitrary large size are unknown. It is conjectured that the solutions disperse as linear waves and enjoy the so-called peeling properties for pointwise estimates. We provide a gauge independent proof of the conjecture.
10 Citations
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#### References

SHOWING 1-10 OF 23 REFERENCES
On global behavior of solutions of the Maxwell-Klein-Gordon equations
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 ofExpand
Time decay of solutions of coupled Maxwell-Klein-Gordon equations
We obtain the optimal time decay of the solutions of the coupled Maxwell-Klein-Gordon equations in four dimensional spacetime, provided the initial data are what we define as Coulomb. In other words,Expand
Time decay of maxwell—klein—gordon equations in 4—dimensional minkowski space
Abstract. In this paper I derive a gauge invariant decay estimate of the solutions of massive Maxwell—Klein—Gordon fields equations in the 4—dimensional Minkowski space, provided that the initialExpand
Asymptotic properties of solutions of the Maxwell Klein Gordon equation with small data
• Mathematics, Physics
• 2014
We prove peeling estimates for the small data solutions of the Maxwell Klein Gordon equations with non-zero charge and with a non-compactly supported scalar field, in $(3+1)$ dimensions. We obtainExpand
Global stability for charged-scalar fields on Minkowski space
• Mathematics
• 2004
We prove that the charge-scalar field (also known as the massless Maxwell-Klein-Gordon) equations are globally stable on (3+1) dimensional Minkowski space for small initial data in certain gaugeExpand
Global Solution for Massive Maxwell‐Klein‐Gordon Equations
• Mathematics, Physics
• Communications on Pure and Applied Mathematics
• 2019
We derive the asymptotic properties of the mMKG system (Maxwell coupled with a massive Klein-Gordon scalar field), in the exterior of the domain of influence of a compact set. This complements theExpand
Asymptotic properties of linear field equations in minkowski space
• Mathematics
• 1990
The aim of this paper is to derive the uniform asymptotic behavior of solutions to linear field equations in Minkowski space, based on geometric consideration and generalized energy estimates. OurExpand
The asymptotic behavior of Yang-Mills fields in the large
• Mathematics
• 1992
We consider Yang-Mills fields in Minkowski space-time and prove that all spherically symmetric solutions in the canonical gauge decay in time, provided the initial data has finite conformal energy.
Asymptotic properties of the solutions of linear and nonlinear spin field equations in Minkowski space
In this paper I will first derive, based on energy estimations and geometric invariance, the asymptotic behavior of solutions of linear spin field equations in Minkowski space. It generalizes theExpand
Uniform decay estimates and the lorentz invariance of the classical wave equation
On etudie le comportement asymptotique des solutions de □u=0 ou □=∂ t 2 −∂ 1 2 ...−∂ n 2 pour des conditions initiales u=0, u t =g(x) en t=0, avec g reguliere a support compact dans R n