Oliver Gough

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math.AP2026

Stable blow-up on a sphere for a quadratic-derivative nonlinear wave equation

Manuel del Pino, Oliver Gough, Monica Musso

We study finite-time blow-up for the nonlinear wave equation \begin{equation*} v_{tt}-Δv=|\nabla_x v|^2 \end{equation*} in dimensions $n \geq 2$ , under radial symmetry. For every pre…

math.AP2025

Stable Type I blow-up for the one-dimensional wave equation with time-derivative nonlinearity

Oliver Gough

We study finite-time blow-up for the one-dimensional nonlinear wave equation with a quadratic time-derivative nonlinearity, \[ u_{tt}-u_{xx}=(u_t)^2,\qquad (x,t)\in\mathbb R\times[…