Strichartz estimates on Kerr black hole backgrounds

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. This follows a local energy decay result for the Kerr space-time obtained in earlier work of Tataru and the author, and uses the techniques and results by the author and collaborators (2010). As an application, we then prove global well-posedness and uniqueness for the energy critical semilinear wave equation with small initial data.