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arXiv · 2004.05664

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

Hans Lindblad·Mihai Tohaneanu
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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 $\Box_{g(u, t, x)} u = 0$ 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 $u$.

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Hans Lindblad, Mihai Tohaneanu. 2020-04-12. A local energy estimate for wave equations on metrics asymptotically close to Kerr. https://doi.org/10.1007/s00023-020-00950-0

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