On blow-up for the supercritical defocusing nonlinear wave equation

In this paper, we consider the defocusing nonlinear wave equation -∂ₜ²u+Δ u=|u|ᵖ⁻¹u in R× Rᵈ. Building on our companion work ({ Self-similar imploding solutions of the relativistic Euler equations}), we prove that for d=4, p≥ 29 and d≥ 5, p≥ 17, there exists a smooth complex-valued solution that blows up in finite time.