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Blow up for harmonic map flow Davila, Juan


We study singularity formation for the harmonic map flow from a two dimensional domain into the sphere. We show that for suit- able initial conditions the flow develops a type 2 singularity at some point in finite time, and that this is stable under small perturbations of the initial condition. This phenomenon and the rate of blow up were studied formally by van den Berg, Hulshof and King (2003) and proved by Raphael and Schweyer (2013) in the class of radial and 1- corrotationally symmetric maps. Our results hold without any symme- try assumptions.

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