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 Wettstein（ETH Zurich）   

题  目：Half-Harmonic Gradient flow - Existence, Uniqueness and Regularity

时  间：2022.06.08（星期三）下午15:00-16:00

地  点：Zoom Meeting: 633 6242 0601  Code: 011227

摘  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.