  The purpose of this article is to establish bounds from below for the life
span of regular solutions to the incompressible Navier-Stokes system,
whichinvolve norms not only of the initial data, but also of nonlinear
functions of the initial data. We provide examples showing that those bounds
are significant improvements to the one provided by the classical fixed point
argument. One of the important ingredients is the use of a scale-invariant
energy estimate.
