Strichartz estimates on Kerr black hole backgrounds
Mihai Tohaneanu
TL;DR
This paper addresses dispersive properties of the linear wave equation on Kerr spacetime with small angular momentum, introducing a global-in-time Strichartz framework. It adapts and extends microlocal and spectral techniques from Minkowski and Schwarzschild settings, notably via refined local energy norms near the photon sphere built from symbols like $b_{ps}$, to overcome trapping and low-frequency difficulties. The main contributions are global Strichartz estimates for $\Box_{\mathbf K}$ (covering nonsharp exponent ranges) and their application to global existence and uniqueness for the energy-critical semilinear wave equation in the exterior region. These results advance the understanding of wave propagation and nonlinear stability on rotating black hole backgrounds and provide a foundation for further Kerr stability analyses.
Abstract
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 then prove global well-posedness and uniqueness for the energy critical semilinear wave equation.