Stability for Rayleigh-Benard convective solutions of the Boltzmann equation
Mathematical Physics
2008-12-22 v1 math.MP
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 2-dimensional convective stationary solution, which is close for small Knudsen number to the convective stationary solution of the Oberbeck-Boussinesq equations, near above the bifurcation point, and prove its stability under 2-d small perturbations, for Rayleigh number above and close to the bifurcation point and for small Knudsen number.
Keywords
Cite
@article{arxiv.0812.3720,
title = {Stability for Rayleigh-Benard convective solutions of the Boltzmann equation},
author = {L. Arkeryd and R. Esposito and R. Marra and A. Nouri},
journal= {arXiv preprint arXiv:0812.3720},
year = {2008}
}