Global Solutions of Wave-Klein--Gordon Systems in 2+1 Dimensional Space-Time with Strong Couplings in Divergence Form

Senhao, Duan,; Ma, Yue

doi:10.1137/20m1377229

Cited by 9 publications

(3 citation statements)

References 16 publications

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“…Such studies are closely related to linear scattering, and the motivations are briefly discussed in the end of §1.2 and in [8,33]. Last, we mention the results [6,9,11,19,22,25,30,32,39] which are also relevant to our study.…”

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confidence: 84%

Global Solution to the Klein--Gordon--Zakharov Equations with Uniform Energy Bounds

Dong¹

2022

SIAM J. Math. Anal.

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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 energy of the solution for this system. The proof relies on Klainerman's vector field and Alinhac's ghost weight methods.The main difficulty originates from the slow decay nature of the Dirac and wave components in three space dimensions. To overcome the difficulty, a sharp understanding of the structure for this system, and a new weighted conformal energy estimate are required. In addition, we also provide a few scattering results for the system.

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confidence: 84%

Global Solution to the Klein--Gordon--Zakharov Equations with Uniform Energy Bounds

Dong¹

2022

SIAM J. Math. Anal.

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“…The hyperboloidal method used in [13] was introduced by Klainerman in [18] to prove global existence results for nonlinear Klein-Gordon equations by using commuting vector fields. Later this method was developed by Klainerman, Wang and Yang [19,24] and by LeFloch and Ma [20,21]; see also [10,11,14].…”

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confidence: 99%

Global stability of the Dirac-Klein-Gordon system in two and three space dimensions

Zhang¹

2023

Preprint

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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 massless Dirac field and a massive scalar field, and prove global existence, sharp time decay estimates and linear scattering for the solutions. In the case of three space dimensions, we consider the Dirac-Klein-Gordon system with a mass parameter in the Dirac equation, and prove uniform (in the mass parameter) global existence, unified time decay estimates and linear scattering in the top order energy space.

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“…In the 3D case, global existence and global behavior were obtained in the pioneering work [35] for small perturbations around 0; in a recent work [25], the authors proved linear scattering for solutions in the energy space with radial symmetry. In the 2D case, very recently the pointwise asymptotic behavior of the small smooth solutions to the system was illustrated; see for instance [14,21,18]. It is worth mentioning that, in [18], the authors obtained a scattering result for the solutions to the Klein-Gordon part of the 2D Klein-Gordon-Zakharov system.…”

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confidence: 99%

Global Behavior of Small Data Solutions for The 2D Dirac-Klein-Gordon Equations

Dong¹,

Kuijie²,

Ma³

et al. 2022

Preprint

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In this paper, we are interested in the two-dimensional Dirac-Klein-Gordon system, which is a basic model in particle physics. We investigate the global behaviors of small data solutions to this system in the case of a massive scalar field and a massless Dirac field. More precisely, our main result is twofold: 1) we show sharp time decay for the pointwise estimates of the solutions which imply the asymptotic stability of this system; 2) we show the linear scattering result of this system which is a fundamental problem when it is viewed as dispersive equations. Our result is valid for general small, highregular initial data, in particular, there is no restriction on the support of the initial data.

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Global Solutions of Wave-Klein--Gordon Systems in 2+1 Dimensional Space-Time with Strong Couplings in Divergence Form

Cited by 9 publications

References 16 publications

Global Solution to the Klein--Gordon--Zakharov Equations with Uniform Energy Bounds

Global Solution to the Klein--Gordon--Zakharov Equations with Uniform Energy Bounds

Global stability of the Dirac-Klein-Gordon system in two and three space dimensions

Global Behavior of Small Data Solutions for The 2D Dirac-Klein-Gordon Equations

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