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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 gauge covariant weighted Sobolev spaces. These…

Analysis of PDEs · Mathematics 2007-05-23 Hans Lindblad , Jacob Sterbenz

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

A conformally invariant model of two interacting massless particles in Minkowski space was proposed by Casalbuoni and Gomis [1]. We generalize this model to the case of de Sitter space from the perspective of geodesic distance, in such a…

High Energy Physics - Theory · Physics 2021-07-20 Naohiro Kanda , Satoshi Okano

The Cauchy problem for the Maxwell-Klein-Gordon equations in Lorenz gauge in $n$ space dimensions ($n \ge 4$) is shown to be locally well-posed for low regularity (large) data. The result relies on the null structure for the main bilinear…

Analysis of PDEs · Mathematics 2018-10-17 Hartmut Pecher

We establish the global existence and scattering for small and localized solutions of the Klein-Gordon-Schr\"{o}dinger system in three dimensions. The system consists of coupled semilinear Schr\"{o}dinger and Klein-Gordon equations with…

Analysis of PDEs · Mathematics 2025-06-13 Chanjin You

We study the 1D Klein-Gordon equation with variable coefficient cubic nonlinearity. This problem exhibits a striking resonant interaction between the spatial frequencies of the nonlinear coefficients and the temporal oscillations of the…

Analysis of PDEs · Mathematics 2014-04-08 Hans Lindblad , Avy Soffer

In this work, we prove global well-posedness and scattering for systems of quadratic nonlinear Schr\"odinger equations in the critical three-dimensional case, for small, localized data. For the terms corresponding to the nonlinearity…

Analysis of PDEs · Mathematics 2023-11-15 Boyang Su

It is commonly accepted that general relativity is the only solution to the consistency problem that appears when trying to build a theory of interacting gravitons (massless spin-2 particles). Padmanabhan's 2008 thought-provoking analysis…

General Relativity and Quantum Cosmology · Physics 2014-06-24 Carlos Barceló , Raúl Carballo-Rubio , Luis J. Garay

We study the Klein-Gordon equation with general interaction term, which may be linear or nonlinear, and space-time dependent. The initial data is general, large and non-radial. We prove that global solutions are asymptotically given by a…

Analysis of PDEs · Mathematics 2023-04-11 Avy Soffer , Xiaoxu Wu

We investigate the effect of the breaking of integrability in the integrals of motion of a sine-Gordon-like system. The class of quasi-integrable models, discussed in the literature, inherits some of the integrable properties they are…

Exactly Solvable and Integrable Systems · Physics 2024-08-20 P. H. S. Palheta , P. E. G. Assis , T. M. N. Gonçalves

We construct and study global solutions for the 3-dimensional incompressible MHD systems with arbitrary small viscosity. In particular, we provide a rigorous justification for the following dynamical phenomenon observed in many contexts:…

Analysis of PDEs · Mathematics 2016-03-29 Ling-Bing He , Li Xu , Pin Yu

In this paper, we propose a globally hyperbolic regularization to the general Grad's moment system in multi-dimensional spaces. Systems with moments up to an arbitrary order are studied. The characteristic speeds of the regularized moment…

Mathematical Physics · Physics 2012-03-05 Zhenning Cai , Yuwei Fan , Ruo Li

We consider both the defocusing and focusing cubic nonlinear Klein--Gordon equations $$ u_{tt} - \Delta u + u \pm u^3 =0 $$ in two space dimensions for real-valued initial data $u(0)\in H^1_x$ and $u_t(0)\in L^2_x$. We show that in the…

Analysis of PDEs · Mathematics 2010-08-17 Rowan Killip , Betsy Stovall , Monica Visan

In this paper we prove the validity of a long wave Whitham approximation for a system consisting of a Boussinesq equation coupled with a Klein-Gordon equation. The proof is based on an infinite series of normal form transformations and an…

Analysis of PDEs · Mathematics 2016-12-23 Wolf-Patrick Düll , Kourosh Sanei Kashani , Guido Schneider

We present a generalized unitarity method for theories of point-particle worldlines coupled to gravity, analogous to that of scattering amplitudes in quantum field theory. This method allows the computation of perturbative observables from…

High Energy Physics - Theory · Physics 2026-02-25 Vincent F. He , Julio Parra-Martinez

We prove global well-posedness for the 3D Klein-Gordon equation with a concentrated nonlinearity.

Analysis of PDEs · Mathematics 2016-07-05 Elena Kopylova

The global attraction is proved for the nonlinear 3D Klein-Gordon equation with a nonlinearity concentrated at one point. Our main result is the convergence of each "finite energy solution" to the manifold of all solitary waves as…

Analysis of PDEs · Mathematics 2019-01-14 Elena Kopylova

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 prove global in time dispersion for the wave and the Klein-Gordon equation inside the Friedlander domain by taking full advantage of the space-time localization of caustics and a precise estimate of the number of waves that may cross at…

Analysis of PDEs · Mathematics 2020-12-16 Oana Ivanovici

We study a class of Hamiltonian deformations of the massless Einstein-Klein-Gordon system in spherical symmetry for which the Dirac constraint algebra closes. The system may be regarded as providing effective equations for quantum…

General Relativity and Quantum Cosmology · Physics 2012-04-24 Andreas Kreienbuehl , Viqar Husain , Sanjeev S. Seahra