Finite-time blow-up of the heat flow of harmonic maps from surfaces

Abstract

This note is concerned with the singular behaviour of solutions to the heat equation of harmonic maps between Riemannian manifolds. Eells and Sampson Recently, Coron-Ghidaglia [3], Ding [4] and Chen-Ding [2] constructed many examples of finite-time blow-up of the solutions in the case where the domain manifold has dimension greater than two.