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  1. ; ; (, Forum of Mathematics, Pi)
    Abstract We consider the harmonic map heat flow for maps$$\mathbb {R}^{2} \to \mathbb {S}^2$$. It is known that solutions to the initial value problem exhibit bubbling along a well-chosen sequence of times. We prove that every sequence of times admits a subsequence along which bubbling occurs. This is deduced as a corollary of our main theorem, which shows that the solution approaches the family of multi-bubble configurations in continuous time. 
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