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On blowup for the supercritical quadratic wave equation

Csobo, Elek; Glogić, Irfan; Schörkhuber, Birgit


We study singularity formation for the focusing quadratic wave equation in the energy supercritical case, i.e., for $d \ge 7$. We find in closed form a new, non-trivial, radial, self-similar blowup solution $u^∗$ which exists for all d $d \ge 7$. For $d = 9$, we study the stability of $u^∗$ without any symmetry assumptions on the initial data and show that there is a family of perturbations which lead to blowup via $u^*$ . In similarity coordinates, this family represents a co-dimension one Lipschitz manifold modulo translation symmetries. In addition, in $d = 7$ and $d = 9$, we prove non-radial stability of the well-known ODE blowup solution. Also, for the first time we establish persistence of regularity for the wave equation in similarity coordinates.

Volltext §
DOI: 10.5445/IR/1000138775
Veröffentlicht am 11.10.2021
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Analysis (IANA)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsmonat/-jahr 09.2021
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000138775
Verlag Karlsruher Institut für Technologie (KIT)
Umfang 63 S.
Serie CRC 1173 Preprint ; 2021/40
Projektinformation SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019)
Externe Relationen Siehe auch
Schlagwörter nonlinear wave equation, singularity formation, self-similar solution
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