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On blow-up for the supercritical defocusing nonlinear wave equation

Year: 2025
Type: article
Abstract: In this paper, we consider the defocusing nonlinear wave equation $-\partial _t^2u+\Delta u=|u|^{p-1}u$ in $\mathbb {R}\times \mathbb {R}^d$ . Building on our companion work (Self-similar imploding solutions of the relativistic Euler equations, arXiv:2403.11471), we prove that for $d=4, p\geq 29$ and $d\geq 5, p\geq 17$ , there exists a smooth complex-valued solution that blows up in finite time.
DOI: 10.1017/fmp.2025.7
Authors: Feng Shao, Dongyi Wei, Zhifei Zhang
Language: English
Open Access status: gold
Estimated APC paid: $2,650
OpenAlex ID: W4408995407
FWCI: 6.418
Cites: 72
Cited by: 4
Related to: 10