Boltzmann方程Rayleigh-Benard对流解的稳定性
Stability for Rayleigh-Benard convective solutions of the Boltzmann equation
摘要：
我们考虑水平平板中气体受引力作用的玻尔兹曼方程。边界条件是扩散型的，规定了壁面温度，因此顶部温度低于底部温度（Benard设置）。本文考虑了一个在分歧点附近的二维对流定解，它在小Knudsen数下与Oberbeck-Boussinesq方程的对流定解接近，并证明了它在Rayleigh数在分歧点上方和附近以及小Knudsen数下在二维小扰动下的稳定性.
英文摘要：
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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