Incompressible navier-stokes-fourier limit of 3d stationary boltzmann equation

. We consider the 3D stationary Boltzmann equation in convex domains with diffuse-reflection boundary condition. We rigorously derive the steady incompressible Navier-Stokes-Fourier system and justify the asymptotic convergence as the Knudsen number & epsilon; shrinks to zero. The proof is based on an intricate analysis of boundary layers with geometric correction and focuses on technical difficulties caused by the singularity in collision kernel k(v, v & PRIME;) and the perturbed remainder estimates.