A Local Energy Estimate for Wave Equations on Metrics Asymptotically Close to Kerr

Hans Lindblad, Mihai Tohaneanu

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

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 □ 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.

Original languageEnglish
Pages (from-to)3659-3726
Number of pages68
JournalAnnales Henri Poincare
Volume21
Issue number11
DOIs
StatePublished - Nov 1 2020

Bibliographical note

Publisher Copyright:
© 2020, Springer Nature Switzerland AG.

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Nuclear and High Energy Physics
  • Mathematical Physics

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