2008/12/19 by L. Arkeryd, Leif Arkeryd, R. Esposito +7
Mathematics · Physics and Astronomy · #82B40 #82C26 #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Gas Dynamics and Kinetic Theory #Mathematical Physics (math-ph) #Numerical methods in inverse problems #math-ph #math.MP #msc:82B40 #msc:82C26
paper · pdf · doi:10.48550/arxiv.0812.3720
arxiv created 2008/12/19 · openalex publication_date 2008/12/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.