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arXiv:math/0005064 [math.AP]AbstractReferencesReviewsResources

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

Terence Tao

Published 2000-05-07, updated 2009-11-28Version 5

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.

Comments: 15 pages, no figures. Some sign and coefficient errors in the equations have been fixed
Journal: JDE 189 (2003), 366-382
Categories: math.AP
Subjects: 35J10
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