Stability of the laminar solution of the Boltzmann equation for the Benard problem
Vol. 3 No. 1 (2008) P.51~P.97
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.
Boltzmann equation, Benard problem, stability
MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 82B40, 82C26
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