Stability of the Laminar Solution of the Boltzmann Equation for the Benard Problem
نویسنده
چکیده
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 1-dimensional stationary solution, which is close for small Knudsen number to the laminar purely conductive stationary solution of the Oberbeck-Boussinesq equations, and prove its stability under small 1-dimensional perturbations and for small Knudsen number.
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