The Strauss conjecture on Kerr black hole backgrounds

Abstract

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.

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References in corpus (8)

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Cited by in corpus (17)

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• The Strauss conjecture on asymptotically flat space-times
• The Glassey conjecture on asymptotically flat manifolds
• Lifespan estimates for local solutions to the semilinear wave equation in Einstein-de Sitter spacetime
• A Vector Field Method for Non-Trapping, Radiating Spacetimes
• Pointwise decay for semilinear wave equations on Kerr spacetimes
• Weighted fractional chain rule and nonlinear wave equations with minimal regularity
• Blow-up and lifespan estimate to a nonlinear wave equation in Schwarzschild spacetime
• Lifespan of solutions to the Strauss type wave system on asymptotically flat space-times
• Localized energy estimates on Myers-Perry space-times
• Lifespan of Solutions to Wave Equations on de Sitter Spacetime
• Nonlinear Wave Equations With Null Condition On Extremal Reissner-Nordström Spacetimes I: Spherical Symmetry
• The Glassey conjecture for nontrapping obstacles
• Sharp decay for Teukolsky equation in Kerr spacetimes
• Lifespan estimates for $2$-dimensional semilinear wave equations in asymptotically Euclidean exterior domains
• Global existence for some 4-D quasilinear wave equations with low regularity