Stable self-similar blow up for energy subcritical wave equations

We consider the semilinear wave equation $\partial_t^2 ψ-Δψ=|ψ|^{p-1}ψ$ for $1<p\leq 3$ with radial data in $\R^{3}$. This equation admits an explicit spatially homogeneous blow up solution $ψ^T$ given by $ψ^T(t,x)=κ_p (T-t)^{-\frac{2}{p-1}}$ where $T>0$ and $κ_p$ is a $p$-dependent constant. We prove that the blow up described by $ψ^T$ is stable against small perturbations in the energy topology. This complements previous results by Merle and Zaag. The method of proof is quite robust and can be applied to other self-similar blow up problems as well, even in the energy supercritical case.

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