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arXiv · 2304.05927

Continuous in time bubble decomposition for the harmonic map heat flow

Jacek Jendrej·Andrew Lawrie·Wilhelm Schlag
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Abstract

We consider the harmonic map heat flow for maps from the plane to the two-sphere. 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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Jacek Jendrej, Andrew Lawrie, Wilhelm Schlag. 2023-04-12. Continuous in time bubble decomposition for the harmonic map heat flow. https://doi.org/10.1017/fmp.2024.15

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