  Consider an exterior space-time domain where the incompressible Navier-Stokes
equation and continuity equation hold with no bodies or force fields present,
and smooth velocity at initial time. This is equivalent to the velocity being
impulsively instantaneously started into motion and further assume that this
force impulse is bounded. A smooth solution with a Stokeslet far-field decay
for all subsequent time is sought and found, demonstrating existence and
smoothness. This is given by a space-time boundary integral velocity
representation by a single layer potential linear distribution of Navier-Stokes
fundamental solutions called NSlets. This is obtained by extending the theory
of hydrodynamic potentials to also include a non-linear potential that
subsequently drops out of the formulation. Zero initial velocity gives the null
solution and so there can be only one smooth solution demonstrating uniqueness
in smooth space, but this is not to say that there are not other possible
solutions in the wider class of non-smooth spaces.
