TY - JOUR
T1 - The Lifespan of Smooth Solutions to Semilinear Wave Equations in Schwarzschild Space-Time
AU - Lou , Qiong
AU - Luo , Shaoying
JO - Journal of Partial Differential Equations
VL - 4
SP - 404
EP - 413
PY - 2023
DA - 2023/11
SN - 36
DO - http://doi.org/10.4208/jpde.v36.n4.6
UR - https://global-sci.org/intro/article_detail/jpde/22137.html
KW - Semilinear wave equations, Schwarzschild spacetime, blow-up, lifespan.
AB - <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>