  The purpose of this paper is to show how the combination of the well-known
results for convergence to equilibrium and conditional regularity, in addition
to a short-time existence result, lead to a quick proof of the existence of
global smooth solutions for the non cutoff Boltzmann equation when the initial
data is close to equilibrium. We include a short-time existence result for
polynomially-weighted $L^\infty$ initial data. From this, we deduce that if the
initial data is sufficiently close to a Maxwellian in this norm, then a smooth
solution exists globally in time.
