A local energy estimate for wave equations on metrics asymptotically close to Kerr

Abstract

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 ${\square }_{g(u,t,x)}u=0$ where the metric $g(u,t,x)$ is close (and asymptotically equal)to a Kerr metric with small angular momentum $g(0,t,x)$. Under suitable assumptions on the metric coefficients, and assuming that the initial data for $u$ is small enough, we prove global existence and decay of the solution $u$.

46 pages

Cited by in corpus (3)

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