Stable blowup for the cubic wave equation in higher dimensions

TL;DR

This paper proves the existence of solutions to the higher-dimensional focusing cubic wave equation that blow up in finite time, approaching a specific blowup profile without symmetry restrictions on initial data.

Contribution

It establishes the existence of open sets of initial data leading to blowup solutions in higher odd dimensions without symmetry assumptions.

Findings

Existence of blowup solutions in higher odd dimensions.

Solutions approach a specific ODE blowup profile.

No symmetry restrictions are needed on initial data.

Abstract

We consider the wave equation with a focusing cubic nonlinearity in higher odd space dimensions without symmetry restrictions on the data. We prove that there exists an open set of initial data such that the corresponding solution exists in a backward light-cone and approaches the ODE blowup profile.