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On continuous time bubbling for the harmonic map heat flow in two dimensions

By Wilhelm Schlag

Appears in collection : Advances in Nonlinear Analysis and Nonlinear Waves, a conference in honor of Frank Merle

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.

Information about the video

  • Date of recording 5/26/23
  • Date of publication 5/31/23
  • Institution IHES
  • Language English
  • Audience Researchers
  • Format MP4


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