相关论文: Decay Estimate of Maxwell-Higgs System on Schwarzs…
This is the second in a series of papers in which we take a systematic study of gauge field theories such as the Maxwell equations and the Yang-Mills equations, on curved space-times. In this paper, we study the Maxwell equations in the…
In this paper we use Morawetz estimates with geometric energy estimates -the so-called vector field method- to prove decay results for the Maxwell field in the static exterior region of the Reissner-Nordstr{\o}m-de Sitter black hole. We…
In this paper, we prove the uniform energy bound for the Maxwell-Higgs system in the exterior region of Reissner-Nordstr\"om black holes. By employing an integrated local energy decay (ILED) estimate in combination with the Sobolev…
A new Morawetz or integrated local energy decay estimate for Maxwell test fields on the exterior of a Schwarzschild black hole spacetime is proved. The proof makes use of a new superenergy tensor $H_{ab}$ defined in terms of the Maxwell…
We study solutions of the decoupled Maxwell equations in the exterior region of a Schwarzschild black hole. In stationary regions, where the Schwarzschild coordinate $r$ ranges over $2M < r_1 < r < r_2$, we obtain a decay rate of $t^{-1}$…
This note surveys how energy generation and strengthening has been used to prove Morawetz estimates for various field equations in Minkowski space, the exterior of the Schwarzschild spacetime, and the exterior of the Kerr spacetime. It…
In this brief note, we consider a wave equation that has both trapping and a complex potential. For this problem, we prove a uniform bound on the energy and a Morawetz (or integrated local energy decay) estimate. The equation is a model…
We prove local energy decay estimates for solutions to the inhomogeneous Maxwell system on a generic class of spherically symmetric black holes.
We provide a uniform decay estimate of Morawetz type for the local energy of general solutions to the inhomogeneous wave equation on a Schwarzchild background. This estimate is both uniform in space and time, so in particular it implies a…
In this article we study the pointwise decay properties of solutions to the Maxwell system on a class of nonstationary asymptotically flat backgrounds in three space dimensions. Under the assumption that uniform energy bounds and a weak…
We consider in this work the asymptotics of a Maxwell field in Schwarzschild and Kerr spacetimes. In any subextremal Kerr spacetime, we show energy and pointwise decay estimates for all components under an assumption of a basic energy and…
We prove uniform decay estimates in the entire exterior of the Schwarzschild black hole for gauge invariant norms on the Yang-Mills fields valued in the Lie algebra associated to the Lie group $SU(2)$. We assume that the initial data are…
We show that a formalism for analyzing the near-horizon conformal symmetry of Schwarzschild black holes using a scalar field probe is capable of describing black hole decay. The equation governing black hole decay can be identified as the…
In this work, we consider solutions of the Maxwell equations on the Schwarzschild-de Sitter family of black hole spacetimes. We prove that, in the static region bounded by black hole and cosmological horizons, solutions of the Maxwell…
We consider the Cauchy problem for the (non-linear) Maxwell-Charged-Scalar-Field equations with spherically symmetric initial data, on a sub-extremal Reissner--Nordstr\"{o}m or Schwarzschild exterior space-time. We prove that the solutions…
We prove sharp pointwise $t^{-3}$ decay for scalar linear perturbations of a Schwarzschild black hole without symmetry assumptions on the data. We also consider electromagnetic and gravitational perturbations for which we obtain decay rates…
We continue our study of the decoupled wave equation in the exterior of a spherically symmetric, Schwarzschild, black hole. Because null geodesics on the photon sphere orbit the black hole, extra effort must be made to show that the high…
In this paper we consider solutions to the linear wave equation on higher dimensional Schwarzschild black hole spacetimes and prove robust nondegenerate energy decay estimates that are in principle required in a nonlinear stability problem.…
In this work, we discuss the generalized Einstein-Maxwell-Dilaton gravity theory with a nonminimal coupling between the Maxwell field and scalar field. Considering different geometric properties of black hole horizon structure, the charged…
We study the wave equation on the real line with a potential that falls off like $|x|^{-\alpha}$ for $|x| \to \infty$ where $2 < \alpha \leq 4$. We prove that the solution decays pointwise like $t^{-\alpha}$ as $t \to \infty$ provided that…