  In this work, along with the companion work Oh (2012), we propose a novel
approach to the problem of gauge choice for the \emph{Yang-Mills equations} on
the Minkowski space $\mathbb{R}^{1+3}$. A crucial ingredient is the associated
\emph{Yang-Mills heat flow}. As this approach does not possess the drawbacks of
the previous approaches (as in Klainerman-Machedon (1995) and Tao (2003)), it
is expected to be more robust and easily adaptable to other settings.
  Building on the results proved in the companion article Oh (2012), we prove,
as one of the first applications of our approach, finite energy global
well-posedness of the Yang-Mills equations on $\mathbb{R}^{1+3}$. This is a
classical result first proved by S. Klainerman and M. Machedon (1995) using
local Coulomb gauges. As opposed to their method, the present approach avoids
the use of Uhlenbeck's lemma (1982), and hence does \emph{not} involve
localization in space-time.
