Gao, CanKrieger, Joachim2014-03-272014-03-272014-03-27201510.3934/cpaa.2015.14.1705https://infoscience.epfl.ch/handle/20.500.14299/102233We prove that the critical Wave Maps equation with target $S^2$ and origin $\R^{2+1}$ admits energy class blow up solutions of the form $\[ u(t, r) = Q(\lambda(t)r) + \eps(t, r) \]$ where $Q:\R^2\rightarrow S^2$ is the ground state harmonic map and $\lambda(t) = t^{-1-\nu}$ for any $\nu>0$. This extends the work $\cite{KST0}$, where such solutions were constructed under the assumption $\nu>\frac{1}{2}$. In light of a result of Struwe $\cite{Struwe1}$, our result is optimal for polynomial blow up rates.critical wave equationhyperbolic dynamicsblowupscatteringstabilityinvariant manifoldtext::journal::journal article::research article