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

Hans Lindblad, Mihai Tohaneanu

Research output: Contribution to journalArticlepeer-review

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

Funding Information:
H.L. was supported in part by NSF grant DMS-1500925 and Simons Collaboration Grant 638955. M.T. was supported in part by the NSF Ggrant DMS–1636435 and Simons collaboration Grant 586051. We would also like to thank the Mittag Leffler Institute for their hospitality during the Fall 2019 program in Geometry and Relativity.

Funding Information:
H.L. was supported in part by NSF grant DMS-1500925 and Simons Collaboration Grant 638955. M.T. was supported in part by the NSF Ggrant DMS–1636435 and Simons collaboration Grant 586051. We would also like to thank the Mittag Leffler Institute for their hospitality during the Fall 2019 program in Geometry and Relativity.

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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