On regularizing-rate estimates for solutions to the heat flow with initial value problem

Abstract

For a compact Riemannian manifold N ⊂ ℝK without boundary, we establish the existence of strong solutions to the heat flow for harmonic maps from ℝn to N, and the regularizing rate estimate of the strong solutions. Moreover, we obtain the analyticity in spatial variables of the solutions. The uniqueness of the mild solutions in C([0, T];W1,n) is also considered in this paper.