Obstructions to the existence of solutions of the self-dual Einstein-Maxwell-Higgs equations on a compact surface

On the spherically symmetric Einstein-Yang-Mills-Higgs equations in Bondi coordinates

We revisit and generalize, to the Einstein-Yang-Mills-Higgs system, previous results of D. Christodoulou and D. Chae concerning global solutions for the Einstein-scalar field and the Einstein-Maxwell-Higgs equations. The novelty of the present work is twofold. For one thing the assumption on the self-interaction potential is improved. For another thing explanation is furnished why the solutions obtained here and those proved by Chae for the Einstein-Maxwell-Higgs decay more slowly than those established by Christodoulou in the case of self-gravitating scalar fields. Actually this latter phenom…

Coulomb 扇区与 Schwarzschild 和慢旋转 Kerr 背景下 Maxwell-Higgs 场的散射

Coulomb Sectors and Scattering for Maxwell-Higgs Fields on Schwarzschild and Slowly Rotating Kerr Backgrounds

针对 Schwarzschild 和慢旋转 Kerr 黑洞外部，发展小数据 Maxwell-Higgs 理论，通过传递原理实现全局存在性、辐射场和散射理论，并识别 Coulomb 扇区中的长程归一化。

Global solvability of massless Dirac-Maxwell systems

We consider the Cauchy problem of massless Dirac-Maxwell equations on an asymptotically flat background and give a global existence and uniqueness theorem for initial values small in an appropriate weighted Sobolev space. The result can be extended via analogous methods to Dirac-Higgs-Yang-Mills theories.

Periodic Maxwell-Chern-Simons vortices with concentrating property

In order to study electrically and magnetically charged vortices in fractional quantum Hall effect and anyonic superconductivity, the Maxwell-Chern-Simons (MCS) model was introduced by [Lee, Lee, Min (1990)] as a unified system of the classical Abelian-Higgs model (AH) and the Chern-Simons (CS) model. In this article, the first goal is to obtain the uniform (CS) limit result of (MCS) model with respect to the Chern-Simons parameter without any restriction on either a particular class of solutions or the number of vortex points. The most important step for this purpose is to derive the relation…

Generic injectivity and stability of inverse problems for connections

We consider the nonlinear problem of determining a connection and a Higgs field from the corresponding parallel transport along geodesics on a Riemannian manifold with boundary, in any dimension. The problem can be reduced to an integral geometry question of some attenuated geodesic ray transform through a pseudolinearization argument. We show injectivity (up to natural obstructions) and stability estimates for both the linear and nonlinear problems for generic simple metrics and generic connections and Higgs fields, including the real-analytic ones. We consider the problems on simple manifold…

The attenuated ray transforms on Gaussian thermostats with negative curvature

In the present paper we consider a Gaussian thermostat on a compact Riemannian surface with negative thermostat curvature. In the case of surfaces with boundary, we show that the thermostat ray transform with attenuation given by a general connection and Higgs field is injective, modulo the natural obstruction, for tensors. We also prove that the connection and Higgs field can be determined, up to a gauge transformation, from the knowledge of the parallel transport between boundary points along all possible thermostat geodesics. In the case of closed surfaces, we obtain similar results for the…

On the global dynamics of Yang-Mills-Higgs equations

We study solutions to the Yang-Mills-Higgs equations on the maximal Cauchy development of the data given on a ball of radius $R$ in $\mathbb{R}^3$. The energy of the data could be infinite and the solution grows at most inverse polynomially in $R-t$ as $t\rightarrow R$. As applications, we derive pointwise decay estimates for Yang-Mills-Higgs fields in the future of a hyperboloid or in the Minkowski space $\mathbb{R}^{1+3}$ for data bounded in the weighted energy space with weights $|x|^{1+ε}$. Moreover, for the abelian case of Maxwell-Klein-Gordon system, we extend the small data result of Li…

带边界的三维弗拉索夫-麦克斯韦系统的长时间动力学

Long-Time Dynamics of the 3D Vlasov-Maxwell System with Boundaries

该研究构造了带边界三维弗拉索夫-麦克斯韦系统的全局时间经典解，通过光锥几何建立新衰减机制，首次得到一般扰动下渐近稳定的非真空定态，为理解带边界的长时间波粒相互作用提供了新框架。