摘要 : 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 ... 展开 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. 收起