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.

56 pages

References in corpus (4)

• Global well-posedness, scattering and blow-up for the energy-critical, focusing, non-linear Schrodinger equation in the radial case
• Ill-posedness for nonlinear Schrodinger and wave equations
• Stable blow up dynamics for the 1-corotational energy critical harmonic heat flow
• Universality of blow up profile for small blow up solutions to the energy critical wave map equation