Krieger, JoachimMiao, Shuang2018-03-082018-03-082018-03-08202010.1215/00127094-2019-0053https://infoscience.epfl.ch/handle/20.500.14299/145276WOS:000514818400002We show that the finite time blow up solutions for the co-rotational Wave Maps problem constructed in [7,15] are stable under suitably small perturbations within the co-rotational class, provided the scaling parameter $λ(t)=t−1−ν$ is sufficiently close to $t−1$, i. e. the constant $ν$ is sufficiently small and positive. The method of proof is inspired by [3,12], but takes advantage of geometric structures of the Wave Maps problem already used in [1,21] to simplify the analysis. In particular, we heavily exploit that the resonance at zero satisfies a natural first order differential equation.critical wave equationblowuptext::journal::journal article::research article