Stability for Rayleigh-Benard convective solutions of the Boltzmann equation
Artikel i vetenskaplig tidskrift, 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

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematik

R. Esposito

Universita degli Studi dell'Aquila

R. Marra

Universita degli Studi di Roma Tor Vergata

A. Nouri

Universite de Provence Aix-Marseille 1

Archive for Rational Mechanics and Analysis

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

Vol. 198 1 125-187