Convergence of Solutions to the Boltzmann Equation in the Incompressible Euler Limit

 We consider here the problem of deriving rigorously, for well-prepared initial data and without any additional assumption, dissipative or smooth solutions of the incompressible Euler equations from renormalized solutions of the Boltzmann equation. This completes the partial results obtained by Golse B. Perthame and L. Desvillettes eds., Series in Applied Mathematics 4 (2000), Gauthier-Villars, Paris] and Lions & Masmoudi Arch. Rational Mech. Anal. 158 (2001), 195–211]. (Accepted June 6, 2002) Published online December 3, 2002 Communicated by Y. BRENIER