Uniqueness and non-uniqueness results of harmonic map flow

Union College Mathematics Conference 2026 (20 mins) — September 2026

PDE seminar, USTC — June 2026

Abstract

Harmonic map flow is the negative gradient flow of the energy functional on the space of Sobolev maps. As a nonlinear parabolic equation, it may fail to admit a unique solution when the initial data are singular. In this talk, I will survey several results concerning uniqueness and nonuniqueness for harmonic map flow. In particular, I will present my recent result establishing nonuniqueness for a broad class of initial maps.