##### Department of Mathematics,

University of California San Diego

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### Colloquium Seminar

## Andrew Lawrie

#### MIT

## Continuous bubbling for the harmonic map heat flow

##### Abstract:

I will discuss joint work with Jacek Jendrej and Wilhelm Schlag about the two dimensional harmonic map heat flow for maps taking values in the sphere. It has been known since the 80s-90’s that solutions can exhibit bubbling along a well-chosen sequence of times — the solution decouples into a superposition of well-separated harmonic maps and a body map accounting for the rest of the energy. We prove that every sequence of times contains a subsequence along which such bubbling occurs. This is deduced as a corollary of our main theorem, which shows that the solution approaches the family of multi-bubbles in continuous time. The proof is partly motivated by the classical theory of dynamical systems and uses the notion of “minimal collision energy” developed in joint work with Jendrej on the soliton resolution conjecture for nonlinear waves.

Host: Ioan Bejenaru

### January 23, 2024

### 4:00 PM

APM 6402

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