FINITE-TIME BLOW-UP OF THE HEAT FLOW OF HARMONIC MAPS FROM SURFACES

This note is concerned with the singular behaviour of solutions to the heat equation of harmonic maps between Riemannian manifolds. Eells and Sampson [5] showed that for C¹ initial values the solutions exist locally in time and asked whether they exist for all time or they may blow up in finite time. 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…