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arXiv · 2306.10667

Asymptotic decay for defocusing semilinear wave equations on Schwarzschild spacetimes

He Mei·Dongyi Wei·Shiwu Yang
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Abstract

In this paper, we study the long time dynamics of solutions to the defocusing semilinear wave equation $\Box_g\phi=|\phi|^{p-1}\phi$ on the Schwarzschild black hole spacetimes. For $\frac{1+\sqrt{17}}{2}<p<5$ and sufficiently smooth and localized initial data, we show that the solution decays like $|\phi|\lesssim t^{-1+\epsilon}$ in the domain of outer communication. The proof relies on the $r$-weighted vector field method of Dafermos-Rodnianski together with the Strichartz estimates for linear waves by Marzuola-Metcalfe-Tataru-Tohaneanu.

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He Mei, Dongyi Wei, Shiwu Yang. 2023-06-19. Asymptotic decay for defocusing semilinear wave equations on Schwarzschild spacetimes. https://arxiv.org/abs/2306.10667

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