Threshold for blowup for the supercritical cubic wave equation

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 $d\ge5$.