On Continuous Time Bubbling for the Harmonic Map Heat Flow in Two Dimensions

26 mai 2023, 11:45
1h
Centre de conférences Marilyn et James Simons (Le Bois-Marie)

Centre de conférences Marilyn et James Simons

Le Bois-Marie

35, route de Chartres 91440 Bures-sur-Yvette

Orateur

Prof. Wilhelm Schlag (Yale University)

Description

I will describe recent work with Jacek Jendrej (CNRS, Paris Nord) and Andrew Lawrie (MIT) on harmonic maps of finite energy from the plane to the two sphere, without making any symmetry assumptions. While it has been known since the 1990s that bubbling occurs along a carefully chosen sequence of times via an elliptic Palais-Smale mechanism, we show that this continues to hold continuously in time. The key notion is that of the “minimal collision energy” which appears in the soliton resolution result by Jendrej and Lawrie on critical equivariant wave maps.

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