We examine solutions to semilinear wave equations on black hole backgrounds and give a proof of an analog of the Strauss conjecture on the Schwarzschild and Kerr, with small angular momentum, black hole backgrounds. The key estimates are a class of weighted Strichartz estimates, which are used near infinity where the metrics can be viewed as small perturbations of the Minkowski metric, and a localized energy estimate on the black hole background, which handles the behavior in the remaining compact set.
|Number of pages||25|
|State||Published - Aug 2014|
Bibliographical noteFunding Information:
The first three authors were supported in part by the NSF. The fifth author was supported by Zhejiang Provincial Natural Science Foundation of China LR12A01002, the Fundamental Research Funds for the Central Universities, NSFC 11301478, 11271322 and J1210038.
ASJC Scopus subject areas
- Mathematics (all)