We consider the Boltzmann equation for a gas in a horizontal slab, subject to
a gravitational force. The boundary conditions are of diffusive type,
specifying the wall temperatures, so that the top temperature is lower than the
bottom one (Benard setup). We consider a 2-dimensional convective stationary
solution, which is close for small Knudsen number to the convective stationary
solution of the Oberbeck-Boussinesq equations, near above the bifurcation
point, and prove its stability under 2-d small perturbations, for Rayleigh
number above and close to the bifurcation point and for small Knudsen number
