Global existence for quasilinear wave equations close to Schwarzschild

Hans Lindblad, Mihai Tohaneanu

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


In this article, we study the quasilinear wave equation (Formula presented.) where the metric g(u,t,x) is close (and asymptotically equal) to the Schwarzschild metric g(0,t,x). Under suitable assumptions of the metric coefficients, and assuming that the initial data for u is small enough, we prove global existence and decay of the solution u. The main technical result of the paper is a local energy estimate for the linear wave equation on metrics with slow decay to the Schwarzschild metric.

Original languageEnglish
Pages (from-to)893-944
Number of pages52
JournalCommunications in Partial Differential Equations
Issue number6
StatePublished - Jun 3 2018

Bibliographical note

Funding Information:
H. L. is supported in part by NSF grant DMS-1500925. M. T. is supported in part by the NSF grant DMS–1636435.

Publisher Copyright:
© 2018, © 2018 Taylor & Francis Group, LLC.


  • Quasilinear wave equation
  • Schwarzschild

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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