Existence and partial regularity results for the heat flow for harmonic maps (Q1107185)

For \(M={\mathbb{R}}^ m \)or compact m-dimensional manifolds M, \(m>2\), and compact n-dimensional target manifolds N we establish the existence of a global, partially regular solution to the evolution problem (1.6-7) for harmonic maps from M into N. The solution is smooth off a singular set of co-dimension \(\geq 2\) and as \(t\to \infty\) converges to a partially regular harmonic map from M into N.