A scaling limit from the wave map to the heat flow into ${\mathbb{S}}^2$

Abstract

In this paper we study a limit connecting a scaled wave map with the heat flow into the unit sphere ${\mathbb{S}}^2$. We show quantitatively how that the two equations are connected by means of an initial layer correction. This limit is motivated as a first step into understanding the limit of zero inertia for the hyperbolic-parabolic Ericksen-Leslie's liquid crystal model.

21 pages