Co-dimension one stable blowup for the supercritical cubic wave equation

For the focusing cubic wave equation, we find an explicit, non-trivial self-similar blowup solution u(T)*, which is defined on the whole space and exists in all supercritical dimensions d >= 5. For d = 7, we analyze its stability properties without any symmetry assumptions and prove the existence of a set of perturbations which lead to blowup via u(T)* in a backward light cone. Moreover, this set corresponds to a co-dimension one Lipschitz manifold modulo translation symmetries in similarity coordinates. (c) 2021 Elsevier Inc. All rights reserved.

Automated summary

This study focuses on the focusing cubic wave equation and identifies an explicit self-similar blowup solution in all supercritical dimensions. Analyzing stability properties in dimension d = 7 without symmetry assumptions, it proves the existence of perturbations leading to blowup. These perturbations correspond to a co-dimension one Lipschitz manifold in similarity coordinates.