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 $d\ge5$.

 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) Externe Relationen Siehe auch
KIT – Die Forschungsuniversität in der Helmholtz-Gemeinschaft
KITopen Landing Page