  In this work, we are interested in the link between strong solutions of the
Boltzmann and the Navier-Stokes equations. To justify this connection, our main
idea is to use information on the limit system (for instance the fact that the
Navier-Stokes equations are globally wellposed in two space dimensions or when
the data are small). In particular we prove that the life span of the solutions
to the rescaled Boltzmann equation is bounded from below by that of the
Navier-Stokes system. We deal with general initial data in the whole space in
dimensions 2 and 3, and also with well-prepared data in the case of periodic
boundary conditions.
