The fluid dynamic limit of the nonlinear boltzmann equation
The fluid dynamic limit of the nonlinear boltzmann equation
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DOI：
10.1002/cpa.3160330506
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发表时间：
1980-09
影响因子：
3
通讯作者：
R. Caflisch
中科院分区：
文献类型：
--
作者：
R. Caflisch
非线性玻尔兹曼方程的解决方案，构造到第一次出现的冲击在相应的流体动力学。这种构造假定了可压缩气体流动的欧拉方程的解的知识。玻尔兹曼解被发现作为一个截断的希尔伯特展开与剩余项，和剩余项解决了弱非线性方程，通过迭代求解。所找到的解具有特殊的初值。它们应该作为“外膨胀”，使初始层、附面层和激波层与之相匹配。
Solutions of the nonlinear Boltzmann equation are constructed up to the first appearance of shocks in the corresponding fluid dynamics. This construction assumes the knowledge of solutions of the Euler equations for compressible gas flow. The Boltzmann solution is found as a truncated Hilbert expansion with a remainder, and the remainder term solves a weakly nonlinear equation which is solved by iteration. The solutions found have special initial values. They should serve as “outer expansions” to which initial layers, boundary layers and shock layers can be matched.