@Article{JPDE-36-4,
author = {Qiong, Lou and Shaoying, Luo},
title = {The Lifespan of Smooth Solutions to Semilinear Wave Equations in Schwarzschild Space-Time},
journal = {Journal of Partial Differential Equations},
year = {2023},
volume = {36},
number = {4},
pages = {404--413},
abstract = {<p style="text-align: justify;">This paper considers the Cauchy problem of the semilinear wave equations
with small initial data in the Schwarzschild space-time, $□_gu = |u_t
| ^p
,$ where $g$ denotes
the Schwarzschild metric. When $1&lt; p&lt;2$ and the initial data are supported far away
from the black hole, we can prove that the lifespan of the spherically symmetric solution obtains the same order as the semilinear wave equation evolving in the Minkowski
space-time by introducing an auxiliary function.</p>},
issn = {2079-732X},
doi = {https://doi.org/10.4208/jpde.v36.n4.6},
url = {https://global-sci.com/article/88097/the-lifespan-of-smooth-solutions-to-semilinear-wave-equations-in-schwarzschild-space-time}
}