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arXiv · 0812.3720

Stability for Rayleigh-Benard convective solutions of the Boltzmann equation

L. Arkeryd·R. Esposito·R. Marra·A. Nouri
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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.

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L. Arkeryd, R. Esposito, R. Marra, A. Nouri. 2008-12-19. Stability for Rayleigh-Benard convective solutions of the Boltzmann equation. https://arxiv.org/abs/0812.3720

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