中科院数学与系统科学研究院

数学研究所

学术报告

偏微分方程研讨班

 

报告人Dr. Jerome WettsteinETH Zurich   

 Half-Harmonic Gradient flow - Existence, Uniqueness and Regularity

  2022.06.08(星期三)下午15:00-16:00

 点:Zoom Meeting: 633 6242 0601  Code: 011227

  要:In this talk, we will discuss some of the results obtained in my PhD work pertaining to the half-harmonic gradient flow which is governed by the non-local PDE:

$$\partial_t u + (-\Delta)^{1/2} u \perp T_u N,$$for functions $u: [0,+\infty[ \times S^1 \to N \subset \mathbb{R}^{K}$. In particular, we shall address questions pertaining to existence of solutions, uniqueness in different senses and regularity as well as a preliminary investigation of bubbling while drawing connections with the nowadays quite classical harmonic gradient flow and the corresponding results proven by Struwe in the 1980’s.

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