报告人：王长友 教授（Purdue University）

时间：6月26日，16:00-17:00

地点：管理科研楼1418

Title: Heat flow of s-harmonic maps into spheres

Abstract: For 0<s<1, s-harmonic maps into manifolds corresponds to the critical points of the Dirichlet s-energy of maps into manifolds $N$. The resulting Euler-Lagrange equation involves a fractional s-Laplace system with supercritical nonlinearities. While they can be viewed as a natural extension of harmonic maps, in which s=1, the analysis of s-harmonic maps tends out to be much more challenging due to the nonlocal features of the equations. In this talk, I will discuss the time-dependent s-harmonic maps, or  $(\partial_t-\Delta)^s u \perp T_u N$. I will present a recent theorem on the partial regularity of suitable weak heat flow of s-harmonic maps. I will describe an existence theorem, joint with Sire and others, when s=1/2.