PERTURBATIVE THEORY FOR THE BOLTZMANN EQUATION IN BOUNDED DOMAINS WITH DIFFERENT BOUNDARY CONDITIONS

We study the Boltzmann equation near a global Maxwellian in the case of bounded domains. We consider the boundary conditions to be either specular reflections or Maxwellian diffusion. Starting from the reference work of Guo [21] in L-x, v(infinity) (1 + vertical bar v vertical bar)(beta) e vertical bar v vertical bar(2)/4), we prove existence, uniqueness, continuity and positivity of solutions for less restrictive weights in the velocity variable; namely, polynomials and stretch exponentials. The methods developed here are constructive.