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Threshold for blowup for the supercritical cubic wave equation

Glogić, Irfan; Maliborski, Maciej; Schörkhuber, Birgit

Abstract:
In this paper, we discuss singularity formation for the focusing cubic wave equation in the energy supercritical regime. For this equation an explicit nontrivial self-similar blowup solution was recently found by the first and third author in [27]. In the seven dimensional case it was proven to be stable along a co-dimension one manifold of initial data. Here, we provide numerical evidence that this solution is in fact a critical solution at the threshold between finite-time blowup and dispersion. Furthermore, we discuss the spectral problem arising in the stability analysis in general dimensions $d\ge5$.

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Volltext §
DOI: 10.5445/IR/1000099947
Veröffentlicht am 18.11.2019
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Analysis (IANA)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsjahr 2019
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000099947
Verlag Karlsruher Institut für Technologie (KIT)
Umfang 17 S.
Serie CRC 1173 Preprint ; 2019/21
Projektinformation SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019)
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