English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

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

Asymptotic decay for defocusing semilinear wave equations on Schwarzschild spacetimes