Abstract
AbstractWe 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 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 𝕊2 target by Merle, Raphaël, and Rodnianski. © 2012 Wiley Periodicals, Inc.
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