ENERGY CONCENTRATION FOR 2-DIMENSIONAL RADIALLY SYMMETRIC EQUIVARIANT HARMONIC MAP HEAT FLOWS

Abstract

We give a description of singularity formation in terms of energy quanta for 2-dimensional radially symmetric equivariant harmonic map heat flows. Adapting Struwe's energy method we first establish a finite bubble tree result with a discrete multiple of energy quanta disappearing in the singularity. We then use intersection-comparison arguments to show that the bubble tree consists of a single bubble only and that there is a well defined scale RBHK(t) ↓ 0 in which the solution converges to the standard harmonic map.