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.
|Number of pages||52|
|Journal||Communications in Partial Differential Equations|
|State||Published - Jun 3 2018|
Bibliographical noteFunding Information:
H. L. is supported in part by NSF grant DMS-1500925. M. T. is supported in part by the NSF grant DMS–1636435.
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- Quasilinear wave equation
ASJC Scopus subject areas
- Applied Mathematics