Pré-Publication, Document De Travail Année : 2023

Continuous in time bubble decomposition for the harmonic map heat flow

Résumé

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.

Dates et versions

hal-04248711 , version 1 (18-10-2023)

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Jacek Jendrej, Andrew Lawrie, Wilhelm Schlag. Continuous in time bubble decomposition for the harmonic map heat flow. 2023. ⟨hal-04248711⟩

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