## 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>>

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