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Exact static, spherically symmetric solutions to the Einstein-Maxwell-scalar equations, with a dilatonic-type scalar-vector coupling, in $D$-dimensional gravity with a chain of $n$ Ricci-flat internal spaces are considered, with the Maxwell…

General Relativity and Quantum Cosmology · Physics 2011-08-17 K. A. Bronnikov

Recently, A. Gruenrock and H. Pecher proved global well-posedness of the 2d Dirac-Klein-Gordon equations given initial data for the spinor and scalar fields in $H^s$ and $H^{s+1/2} \times H^{s-1/2}$, respectively, where $s\ge 0$, but…

Analysis of PDEs · Mathematics 2011-09-26 Sigmund Selberg , Achenef Tesfahun

We give a new proof of the global stability of Minkowski space originally established in the vacuum case by Christodoulou and Klainerman. The new approach shows that the Einstein-vacuum and the Einstein-scalar field equations with general…

Analysis of PDEs · Mathematics 2010-01-03 Hans Lindblad , Igor Rodnianski

In this article, we use an electromagnetic gauge-free framework to establish the existence of small-data global solutions to the Maxwell-Born-Infeld (MBI) system on the Minkowski space background in 1 + 3 dimensions. Because the…

Mathematical Physics · Physics 2015-05-19 Jared Speck

In this paper, a Hamiltonian lattice formulation for 2+1D compact Maxwell-Chern-Simons theory is derived. We analytically solve this theory and demonstrate that the mass gap in the continuum limit matches the well-known continuum formula.…

The Cauchy problem for the Chern-Simons-Higgs system in the (2+1)-dimensional Minkowski space in temporal gauge is locally well-posed for low regularity initial data improving a result of Huh. The proof uses the bilinear space-time…

Analysis of PDEs · Mathematics 2014-10-16 Hartmut Pecher

In this paper, we provide a much simplified proof of the main result in [Lin, Xu, Zhang, arXiv:1302.5877] concerning the global existence and uniqueness of smooth solutions to the Cauchy problem for a 2D incompressible viscous and…

Analysis of PDEs · Mathematics 2014-10-24 Ting Zhang

We obtain and study static, spherically symmetric solutions for the Einstein - generalized Maxwell field system in 2n dimensions, with possible inclusion of a massless scalar field. The generalization preserves the conformal invariance of…

General Relativity and Quantum Cosmology · Physics 2011-04-15 Kirill A. Bronnikov , Julio Cesar Fabris

In this article, we study the coupling of the Einstein field equations of general relativity to a family of models of nonlinear electromagnetic fields. The family comprises all covariant electromagnetic models that satisfy the following…

Analysis of PDEs · Mathematics 2016-01-20 Jared Speck

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

In recent years, the global existence of classical solutions to the Cauchy problem for 2D incompressible viscous MHD equations without magnetic diffusion has been proved in \cite{Ren,TZhang}, under the assumption that initial data is close…

Analysis of PDEs · Mathematics 2025-05-22 Shijin Ding , Ronghua Pan , Yi Zhu

We show that in dimensions $n \geq 6$ that one has global regularity for the Maxwell-Klein-Gordon equations in the Coulomb gauge provided that the critical Sobolev norm $\dot H^{n/2-1} \times \dot H^{n/2-2}$ of the initial data is…

Analysis of PDEs · Mathematics 2009-11-10 Igor Rodnianski , Terence Tao

We derive the global dynamic properties of the mMKG system (Maxwell coupled with a massive Klein-Gordon scalar field) with a general, unrestrictive class of data, in particular, for Maxwell field of arbitrary size, and by a gauge…

Analysis of PDEs · Mathematics 2019-02-26 Allen Fang , Qian Wang , Shiwu Yang

As a continuation of our series works on the Boltzmann equation without angular cutoff assumption, in this part, the global existence of solution to the Cauchy problem in the whole space is proved in some suitable weighted Sobolev spaces…

Analysis of PDEs · Mathematics 2010-10-28 Radjesvarane Alexandre , Y. Morimoto , Seiji Ukai , Chao-Jiang Xu , Tong Yang

We consider the Maxwell-Chern-Simons-Higgs system in Lorenz gauge and use a null condition to show local well-psoedness for low regularity data. This improves a recent result of J. Yuan.

Analysis of PDEs · Mathematics 2015-06-16 Hartmut Pecher

We prove global existence for solutions arising from small initial data for a large class of quasilinear wave equations satisfying the `weak null condition' of Lindblad and Rodnianski, significantly enlarging upon the class of equations for…

Analysis of PDEs · Mathematics 2018-10-02 Joseph Keir

Here we prove a global existence theorem for the solutions of the semi-linear wave equation with critical non-linearity admitting a positive definite Hamiltonian. Formulating a parametrix for the wave equation in a globally hyperbolic…

General Relativity and Quantum Cosmology · Physics 2021-10-04 Puskar Mondal

Minkowski space is shown to be globally stable as a solution to the massive Einstein--Vlasov system. The proof is based on a harmonic gauge in which the equations reduce to a system of quasilinear wave equations for the metric, satisfying…

General Relativity and Quantum Cosmology · Physics 2017-11-07 Hans Lindblad , Martin Taylor

We obtain a class of magnetically charged solutions in 2+1 dimensional Einstein - Power - Maxwell theory. In the linear Maxwell limit, such horizonless solutions are known to exist. We show that in 3D geometry, black hole solutions with…

General Relativity and Quantum Cosmology · Physics 2011-12-19 S. Habib Mazharimousavi , O. Gurtug , M. Halilsoy , O. Unver

We prove in the cases of spherical, plane and hyperbolic symmetry a local in time existence theorem and continuation criteria for cosmological solutions of the Einstein-Vlasov-scalar field system, with the sources generated by a…

General Relativity and Quantum Cosmology · Physics 2007-05-23 David Tegankong , Norbert Noutchegueme , Alan D. Rendall