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

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

2000-05-07

arxiv.org/abs/math/0005064v5

JDE 189 (2003), 366-382

Mathematics

Analysis of PDEs

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

Scientific paper

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.

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