相关论文: Physical-space estimates for axisymmetric waves on…

In this paper, we prove energy and Morawetz estimates for solutions to the scalar wave equation in spacetimes with metrics that are perturbations, compatible with nonlinear applications, of Kerr metrics in the full subextremal range.…

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 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 consider solutions to the linear wave equation in the interior region of extremal Kerr black holes. We show that axisymmetric solutions can be extended continuously beyond the Cauchy horizon and moreover that, if we assume suitably fast…

On the full range of sub-extremal Kerr exterior spacetimes we give a new proof of energy boundedness for high-frequency projections of solutions to the wave equation onto trapped frequencies. A key feature of the new estimate is that it…

We study the Cauchy problem for the wave equation on extreme Kerr backgrounds under axisymmetry. Specifically, we consider regular axisymmetric initial data prescribed on a Cauchy hypersurface S which connects the future event horizon with…

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…

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}…

In this paper, we prove energy and Morawetz estimates for solutions to Teukolsky equations in spacetimes with metrics that are perturbations, compatible with nonlinear applications, of Kerr metrics in the full subextremal range. The…

We consider Morawetz estimates for weighted energy decay of solutions to the wave equation on scattering manifolds (i.e., those with large conic ends). We show that a Morawetz estimate persists for solutions that are localized at low…

In this article we prove a local energy estimate for the linear wave equation on metrics with slow decay to a Kerr metric with small angular momentum. As an application, we study the quasilinear wave equation $\Box_{g(u, t, x)} u = 0$ where…

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 consider gravity water waves in two space dimensions, with finite or infinite depth. Assuming some uniform scale invariant Sobolev bounds for the solutions, we prove local energy decay (Morawetz) estimates globally in time. Our result is…

This document proves global boundedness and decay for axisymmetric perturbations of a known solution to the wave map problem from a slowly rotating $|a|\ll M$ Kerr spacetime to the hyperbolic plane. This problem is motivated by the general…

This second part of the series treats spin $\pm2$ components (or extreme components), that satisfy the Teukolsky master equation, of the linearized gravity in the exterior of a slowly rotating Kerr black hole. For each of these two…

We study dispersive properties for the wave equation in the Kerr space-time with small angular momentum. The main result of thispaper is to establish uniform energy bounds and local energy decay for such backgrounds.

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…

We obtain remarkably simple integral bounds for axially symmetric linear perturbations for the extreme Kerr black hole in terms of conserved energies. From these estimates we deduce pointwise bounds for the perturbations outside the…

We study the dispersive properties for the wave equation in the Kerr space-time with small angular momentum. The main result of this paper is to establish Strichartz estimates for solutions of the aforementioned equation. As an application,…

We study the Klein--Gordon equation $\Box_{g_{a,M,l}}\psi-\mu^2_{\textit{KG}}\psi=0$ on subextremal Kerr--de Sitter black hole backgrounds with parameters $(a,M,l)$, where $l^2=\frac{3}{\Lambda}$. We prove boundedness and Morawetz estimates…