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We study the blow-up dynamics for the energy-critical 1-corotational wavemaps problem with 2-sphere target. In arXiv:0911.0692, Rapha\"el and Rodnianskiexhibited a stable finite time blow-up dynamics arising from smooth initialdata. In this paper, we exhibit a sequence of new finite-time blow-up rates(quantized rates), which can still arise from well-localized smooth initialdata. We closely follow the strategy of the paper arXiv:1301.1859 by Rapha\"eland Schweyer, who exhibited a similar construction of the quantized blow-uprates for the harmonic map heat flow. The main difficulty in our wave mapssetting stems from the lack of dissipation and its critical nature, which weovercome by a systematic identification of correction terms in higher-orderenergy estimates.

Quantized slow blow-up dynamics for the energy-critical corotational wave maps problem