On blow-up for the supercritical defocusing nonlinear wave equation

Abstract

In this paper, we consider the defocusing nonlinear wave equation $-{\partial }_t^{2}u+\Delta u=|u{|}^{p-1}u$ 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 $d=4,p\ge 29$ and $d\ge 5,p\ge 17$, there exists a smooth complex-valued solution that blows up in finite time.

arXiv comment56 pages

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