Local well-posedness of the Yang-Mills equation in the Temporal Gauge below the energy norm
Terence Tao
Abstract
We show that the Yang-Mills equation in three dimensions is locally well-posed in the Temporal gauge for initial data in Hs x Hs-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 partialt u = F.
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