[{"type":"report","title":"Co-dimension one stable blowup for the supercritical cubic wave equation","issued":{"date-parts":[["2018"]]},"DOI":"10.5445\/IR\/1000088078","author":[{"family":"Glogi\u0107","given":"Irfan"},{"family":"Sch\u00f6rkhuber","given":"Birgit"}],"publisher":"Karlsruher Institut f\u00fcr Technologie (KIT)","ISSN":"2365-662X","collection-title":"CRC 1173","abstract":"For the focusing cubic wave equation, we find an explicit, non-trivial self-similar blowup solution u^\u2217_T , which is defined on the whole space and exists in all supercritical dimensions d \u2265 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^\u2217_T (modulo space-time shifts and Lorentz boosts) in the backward lightcone of the blowup point. The underlying topology is strictly above scaling.","keyword":"nonlinear wave equation, supercritical, blowup, self-similar, stability","number-of-pages":47,"kit-publication-id":"1000088078"}]