## Type II solutions Type II blow up solutions with optimal stability properties for the critical focussing nonlinear wave equation on $\R^{3+1}$

We show that the finite time type II blow up solutions for the energy critical nonlinear wave equation $\Box u = -u^5$ on $\R^{3+1}$ constructed in \cite{KST}, \cite{KS1} are stable along a co-dimension one Lipschitz manifold of data perturbations in a suitable topology, provided the scaling parameter $\lambda(t) = t^{-1-\nu}$ is sufficiently close to the self-similar rate, i. e. $\nu>0$ is sufficiently small. This result is qualitatively optimal in light of the result of \cite{CNLW4}. The paper builds on the analysis of \cite{CondBlow}.

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.....submitted in 2017 October
Year:
2018
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