Year: 2023
Author: Qiong Lou, Shaoying Luo
Journal of Partial Differential Equations, Vol. 36 (2023), Iss. 4 : pp. 404–413
Abstract
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 $1< p<2$ 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jpde.v36.n4.6
Journal of Partial Differential Equations, Vol. 36 (2023), Iss. 4 : pp. 404–413
Published online: 2023-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 10
Keywords: Semilinear wave equations Schwarzschild spacetime blow-up lifespan.