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The Strauss Conjecture On Kerr Black Hole Backgrounds, Hans Lindblad, Jason Metcalfe, Christopher D. Sogge, Mihai H. Tohaneanu, Chengo Wang
The Strauss Conjecture On Kerr Black Hole Backgrounds, Hans Lindblad, Jason Metcalfe, Christopher D. Sogge, Mihai H. Tohaneanu, Chengo Wang
Mihai H. Tohaneanu
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.
Price's Law On Nonstationary Space-Times, Jason Metcalfe, Daniel Tataru, Mihai H. Tohaneanu
Price's Law On Nonstationary Space-Times, Jason Metcalfe, Daniel Tataru, Mihai H. Tohaneanu
Mihai H. Tohaneanu
In this article, we study the pointwise decay properties of solutions to the wave equation on a class of nonstationary asymptotically flat backgrounds in three space dimensions. Under the assumption that uniform energy bounds and a weak form of local energy decay hold forward in time we establish a t-3 local uniform decay rate (Price's law, Price 1972) for linear waves. As a corollary, we also prove Price's law for certain small perturbations of the Kerr metric. This result was previously established by the second author in (Tataru) on stationary backgrounds. The present work was motivated by the problem of …
A Local Energy Estimate On Kerr Black Hole Backgrounds, Daniel Tataru, Mihai H. Tohaneanu
A Local Energy Estimate On Kerr Black Hole Backgrounds, Daniel Tataru, Mihai H. Tohaneanu
Mihai H. Tohaneanu
We study dispersive properties for the wave equation in the Kerr space–time with small angular momentum. The main result of this paper is to establish uniform energy bounds and local energy decay for such backgrounds. This follows similar results for the Schwarzschild space–time proved earlier in [3], [8], and [16] and extended in earlier work [29] of the authors and collaborators.
Strichartz Estimates On Schwarzschild Black Hole Backgrounds, Jeremy Marzoula, Jason Metcalfe, Daniel Tataru, Mihai H. Tohaneanu
Strichartz Estimates On Schwarzschild Black Hole Backgrounds, Jeremy Marzoula, Jason Metcalfe, Daniel Tataru, Mihai H. Tohaneanu
Mihai H. Tohaneanu
We study dispersive properties for the wave equation in the Schwarzschild space-time. The first result we obtain is a local energy estimate. This is then used, following the spirit of [29], to establish global-in-time Strichartz estimates. A considerable part of the paper is devoted to a precise analysis of solutions near the trapping region, namely the photon sphere.