Stability of the laminar solution of the Boltzmann equation for the Benard problem
by L. Arkeryd   R. Esposito   R. Marra   A. Nouri  

Vol. 3 No. 1 (2008) P.51~P.97

ABSTRACT

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.

KEYWORDS
Boltzmann equation, Benard problem, stability

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 82B40, 82C26

MILESTONES

Received: 2007-09-21
Revised :
Accepted:

Download Full Content