From the Boltzmann equations to the equations of incompressible fluid mechanics, II

We consider here the problem of deriving rigorously from renormalized solut ions of Boltzmann's equation, globally in time, for general initial conditi ons and without any additional assumption, solutions of Stokes' equations ( together with the strong Boussinesq relation). We also obtain similar resul ts for Euler equations where, however, we need to make an assumption on the high velocities of the solutions of Boltzmann's equation.