Stability for Rayleigh-Benard convective solutions of the Boltzmann equation
Journal article, 2010

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 for small Knudsen numbers is close to the convective stationary solution of the Oberbeck-Boussinesq equations, near and above the bifurcation point, and prove its stability under 2-d small perturbations, for Rayleigh numbers above and close to the bifurcation point and for small Knudsen numbers.


Leif Arkeryd

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

R. Esposito

University of L'Aquila

R. Marra

University of Rome Tor Vergata

A. Nouri

Aix Marseille University

Archive for Rational Mechanics and Analysis

0003-9527 (ISSN) 1432-0673 (eISSN)

Vol. 198 1 125-187

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