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DOI: 10.5445/IR/1000088078
Veröffentlicht am 03.12.2018

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

Glogić, Irfan; Schörkhuber, Birgit

Abstract:
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 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.


Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht
Jahr 2018
Sprache Englisch
Identifikator ISSN: 2365-662X
URN: urn:nbn:de:swb:90-880786
KITopen-ID: 1000088078
Verlag KIT, Karlsruhe
Umfang 47 S.
Serie CRC 1173 ; 2018/39
Projektinformation SFB 1173/1 (DFG, DFG KOORD, SFB 1173/1 2015)
Schlagworte nonlinear wave equation, supercritical, blowup, self-similar, stability
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