Co-dimension one stable blowup for the supercritical cubic wave equation. (arXiv:1810.07681v1 [math.AP])
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 $d \geq 5$. For $d=7$, we analyze its
stability properties without any symmetry assumptions and prove the existence
of a co-dimension one Lipschitz manifold consisting of initial data whose
solutions blowup in finite time and converge asymptotically to $u^*_T$ (modulo
space-time shifts and Lorentz boosts) in the backward lightcone of the blowup
point. The underlying topology is strictly above scaling.查看全文