Stable Blowup Dynamics for the 1-Corotational Energy Critical Harmonic Heat Flow

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Abstract

We exhibit a stable finite time blowup regime for the 1-corotational energy critical harmonic heat flow from ℝ2 into a smooth compact revolution surface of ℝ3 that reduces to the semilinear parabolic problem

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for a suitable class of functions f. The corresponding initial data can be chosen smooth, well localized, and arbitrarily close to the ground state harmonic map in the energy-critical topology. We give sharp asymptotics on the corresponding singularity formation that occurs through the concentration of a universal bubble of energy at the speed predicted by van den Berg, Hulshof, and King. Our approach lies in the continuation of the study of the 1-equivariant energy critical wave map and Schrödinger map with ��2 target by Merle, Raphaël, and Rodnianski. © 2012 Wiley Periodicals, Inc.

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