相关论文: A note on integrated local energy decay estimates …

We present a new general method for proving global decay of energy through a suitable spacetime foliation, as well as pointwise decay, starting from an integrated local energy decay estimate. The method is quite robust, requiring only…

We give an elementary new argument for global existence and exponential decay of solutions of quasilinear wave equations on Schwarzschild-de Sitter black hole backgrounds, for appropriately small initial data. The core of the argument is…

Localized energy estimates for the wave equation have been increasingly used to prove various other dispersive estimates. This article focuses on proving such localized energy estimates on $(1+4)$-dimensional Myers-Perry black hole…

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…

We use a novel physical space method to prove relatively non-degenerate integrated energy estimates for the wave equation on subextremal Schwarzschild-de Sitter spacetimes with parameters $(M,\Lambda)$. These are integrated decay statements…

We prove the existence of exponentially accurate quasimodes using the square of the Dirac operator on the Schwarzschild-Anti-de Sitter spacetime and the Agmon estimates. We then deduce a logarithmic lower bound for the local energy decay of…

We show that it is possible to embed the 1+1 dimensional reduction of certain spherically symmetric black hole spacetimes into 2+1 Minkowski space. The spacetimes of interest (Schwarzschild de-Sitter, Schwarzschild anti de-Sitter, and…

We prove local energy decay estimates for solutions to the inhomogeneous Maxwell system on a generic class of spherically symmetric black holes.

Quasi-local energies for constantly accelerating observers in Ba\~nados, Teitelboim, and Zanelli (BTZ), Schwarzschild and Schwarzschild-de Sitter spacetimes are derived. The energies are expressed in terms of acceleration, cosmological…

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 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…

We prove integrated local energy decay for the damped wave equation on stationary, asymptotically flat space-times in (1 + 3) dimensions. Local energy decay constitutes a powerful tool in the study of dispersive partial differential…

This paper contains the first two parts (I-II) of a three-part series concerning the scalar wave equation \Box_g{\psi} = 0 on a fixed Kerr background. We here restrict to two cases: (II1) |a| \ll M, general {\psi} or (II2) |a| < M, {\psi}…

We investigate static spherically symmetric solutions within the framework of the local limit of nonlocal gravity. This theory departs from Einstein's general relativity (GR) through the introduction of a scalar gravitational susceptibility…

The localized energy estimate for the wave equation is known to be a fairly robust measure of dispersion. Recent analogs on the $(1+3)$-dimensional Schwarzschild space-time have played a key role in a number of subsequent results, including…

This is the first part of a series of papers deriving the precise, late-time behaviour and (in)stability properties of charged scalar fields on near-extremal Reissner--Nordstr\"om spacetimes via energy estimates. In this paper, we establish…

The Schwarzschild and Reissner-Nordstrom solutions to Einstein's equations describe space- times which contain spherically symmetric black holes. We consider solutions to the linear wave equation in the exterior of a fixed black hole space-…

We prove boundedness and inverse logarithmic decay in time of solutions to the Teukolsky equations on Schwarzschild-Anti-de Sitter backgrounds with standard boundary conditions originating from fixing the conformal class of the non-linear…

We present an elementary physical space argument to establish local integrated decay estimates for the perturbed wave equation $\Box_g \phi = \epsilon \beta^a \partial_a \phi$ on the exterior of the Schwarzschild geometry $(\mathcal{M},g)$.…

We study dispersive properties for the wave equation in the Schwarzschild space-time. The first result we obtain is a local energy estimate. This is then used, following the spirit of earlier work of Metcalfe-Tataru, in order to establish…