# Threshold for blowup for the supercritical cubic wave equation

@article{Glogic2019ThresholdFB, title={Threshold for blowup for the supercritical cubic wave equation}, author={Irfan Glogic and Maciej Maliborski and Birgit Sch{\"o}rkhuber}, journal={ArXiv}, year={2019}, volume={abs/1905.13739} }

In this paper, we discuss singularity formation for the fo-
cusing 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…

## 5 Citations

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

- Mathematics, Physics
- 2018

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 $d \geq 5$.…

On blowup for the supercritical quadratic wave equation

- Mathematics, Physics
- 2021

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…

Self-similar solutions of energy-supercritical focusing wave equations in all dimensions

- Physics, Mathematics
- 2020

In this paper, we prove the existence of a countable family of regular spherically symmetric self-similar solutions to focusing energy super-critical semi-linear wave equations \begin{equation*}
…

Self-similar solutions of focusing semi-linear wave equations in $${\mathbb {R}}^{N}$$

- MathematicsJournal of Evolution Equations
- 2021

In this paper, we prove the existence of a countable family of regular spherically symmetric self-similar solutions to focusing energy-supercritical semi-linear wave equations $$\begin{aligned}…

Dynamics at the threshold for blowup for supercritical wave equations outside a ball

- MathematicsNonlinearity
- 2020

We consider spherically symmetric supercritical focusing wave equations outside a ball. Using mixed analytical and numerical methods, we show that the threshold for blowup is given by a…

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