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arXiv · 2405.19674

On blow-up for the supercritical defocusing nonlinear wave equation

Feng Shao·Dongyi Wei·Zhifei Zhang
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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 ({\it \small Self-similar imploding solutions of the relativistic Euler equations}), 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.

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Feng Shao, Dongyi Wei, Zhifei Zhang. 2024-05-30. On blow-up for the supercritical defocusing nonlinear wave equation. https://doi.org/10.1017/fmp.2025.7

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