## Stable blow up dynamics for energy supercritical wave equations    [PDF]

Roland Donninger, Birgit Schörkhuber
We study the semilinear wave equation $\partial_t^2 \psi-\Delta \psi=|\psi|^{p-1}\psi$ for $p > 3$ with radial data in three spatial dimensions. There exists an explicit solution which blows up at $t=T>0$ given by $\psi^T(t,x)=c_p (T-t)^{-\frac{2}{p-1}}$ where $c_p$ is a suitable constant. We prove that the blow up described by $\psi^T$ is stable in the sense that there exists an open set (in a topology strictly stronger than the energy) of radial initial data that lead to a solution which converges to $\psi^T$ as $t\to T-$ in the backward lightcone of the blow up point $(t,r)=(T,0)$.
View original: http://arxiv.org/abs/1207.7046