A Scaling Limit from the Wave Map to the Heat Flow Into S2

Abstract

In this paper we study a limit connecting a scaled wave map with the heat flow into the unit sphere 𝕊2. We show quantitatively how 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.