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

Abstract

For the focusing cubic wave equation, we find an explicit, non-trivial self-similar blowup solution uT⁎, 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 uT⁎ in a backward light cone. Moreover, this set corresponds to a co-dimension one Lipschitz manifold modulo translation symmetries in similarity coordinates.