Global analysis of quasilinear wave equations on asymptotically Kerr-de Sitter spaces

Abstract

We extend the semilinear framework developed by the two authors and the non-trapping quasilinear theory developed by the first author to solve quasilinear wave equations with normally hyperbolic trapping. The most well-known example that fits into our general framework is wave-type equations on Kerr-de Sitter space. The key advance is an adaptation of the Nash-Moser iteration to our framework.