On blow-up for the supercritical defocusing nonlinear wave equation

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.