Continuous in time bubble decomposition for the harmonic map heat flow
Analysis of PDEs
2025-02-19 v1 Differential Geometry
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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Cite
@article{arxiv.2304.05927,
title = {Continuous in time bubble decomposition for the harmonic map heat flow},
author = {Jacek Jendrej and Andrew Lawrie and Wilhelm Schlag},
journal= {arXiv preprint arXiv:2304.05927},
year = {2025}
}
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36 pages