  This short proof shows that for smooth and sufficiently fast decaying initial
data at infinity, the full incompressible Navier-Stokes solutions are eternal.
The proof uses an orthogonal decomposition of the velocity field and some
well-known vector calculus identities to establish a particular contradiction,
which leads to a vanishing integral, which is the main integral that determines
the evolution of enstrophy. As it is shown that enstrophy is non-increasing, it
is well-know that the solutions stay regular at all times.
