Equilibrating Effect of Maxwell-Type Boundary Condition in Highly Rarefied Gas

研究成果: Article同行評審

3 引文 斯高帕斯(Scopus)

摘要

We study the equilibrating effects of the boundary and intermolecular collision in the kinetic theory for rarefied gases. We consider the Maxwell-type boundary condition, which has weaker equilibrating effect than the commonly studied diffuse reflection boundary condition. The gas region is the spherical domain in (Formula presented.)=1,2. First, without the equilibrating effect of the collision, we obtain the algebraic convergence rates to the steady state of free molecular flow with variable boundary temperature. The convergence behavior has intricate dependence on the accommodation coefficient of the Maxwell-type boundary condition. Then we couple the boundary effect with the intermolecular collision and study their interaction. We are able to construct the steady state solutions of the full Boltzmann equation for large Knudsen numbers and small boundary temperature variation. We also establish the nonlinear stability with exponential rate of the stationary Boltzmann solutions. Our analysis is based on the explicit formulations of the boundary condition for symmetric domains.

原文English
頁(從 - 到)743-800
頁數58
期刊Journal of Statistical Physics
161
發行號3
DOIs
出版狀態Published - 2015 十一月 1

All Science Journal Classification (ASJC) codes

  • 統計與非線性物理學
  • 數學物理學

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