Local well-posedness of the Yang-Mills equation in the Temporal Gauge below the energy norm

Abstract

We show that the Yang-Mills equation in three dimensions is locally well-posed in the Temporal gauge for initial data in H^s x H^{s-1} for s > 3/4, if the norm of the initial data is sufficiently small. The main new ingredients are a splitting of the connection into curl-free and div-free components, and some product estimates which interact solutions of wave equations Box u = F with solutions of time integration equations partial_t u = F.

15 pages, no figures. Some sign and coefficient errors in the equations have been fixed