Convergence Rate to Stationary Solutions for Boltzmann Equation with External Force*
Convergence Rate to Stationary Solutions for Boltzmann Equation with External Force*
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DOI：
10.1007/s11401-005-0199-4
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发表时间：
2006-08
期刊：
影响因子：
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通讯作者：
S. Ukai;Tong Yang;Huijiang Zhao
中科院分区：
文献类型：
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作者：
S. Ukai;Tong Yang;Huijiang Zhao
摘要S. Ukai et al.（2005）对空间变量中具有势函数梯度形式的外力的Boltzmann方程，利用能量法研究了其作为局部麦克斯韦方程组的平稳解的稳定性。本文在此稳定性分析的基础上，结合可压缩Navier-Stokes方程稳态解的收敛速率分析技术，研究了非平衡稀薄气体统计物理中的基本方程Boltzmann方程的上述稳态解的收敛速率。通过著名的h定理，将流体分量上的黏度和导热耗散与非流体分量上的耗散结合起来，通过构造一些能量泛函，得到了与可压缩Navier-Stokes相同阶的收敛速率。
AbstractFor the Boltzmann equation with an external force in the form of the gradient of a potential function in space variable, the stability of its stationary solutions as local Maxwellians was studied by S. Ukai et al. (2005) through the energy method. Based on this stability analysis and some techniques on analyzing the convergence rates to station- ary solutions for the compressible Navier-Stokes equations, in this paper, we study the convergence rate to the above stationary solutions for the Boltzmann equation which is a fundamental equation in statistical physics for non-equilibrium rarefied gas. By combining the dissipation from the viscosity and heat conductivity on the fluid components and the dissipation on the non-fluid component through the celebrated H-theorem, a convergence rate of the same order as the one for the compressible Navier-Stokes is obtained by constructing some energy functionals.