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MATHEMATICAL AND PHYSICAL STUDIES ON SINGULAR FLUID-DYNAMIC LIMITS FOR THE BOLTZMANN EQUATION

Boltzmann方程奇异流体动力极限的数学和物理研究

基本信息

批准号：
14350047
负责人：
AOKI Kazuo
金额：
$ 9.22万
依托单位：
KYOTO UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
2002
资助国家：
日本
起止时间：
2002 至 2004
项目状态：
已结题

项目摘要

1.Flows of a vapor with evaporation and condensation on the boundary was considered in the presence of a tiny amount of an inert gas. New type of fluid dynamics describing such flows was derived systematically by considering the fluid-dynamic limit of the Boltzmann equation and its boundary condition. The new fluid dynamics revealed the fact that the presence of the inert gas with an infinitesimal average concentration has a significant effect on the overall vapor flow.2.A binary mixture of vapors evaporating from the plane condensed phase and flowing toward infinity and the same mixture flowing from infinity and condensing on the plane condensed phase (half-space problem) were investigated on the basis of kinetic theory. First, the case of weak evaporation and condensation was considered. The flow of the vapors and the relationship among the parameters (associated with the condensed phase and the vapors at infinity) were clarified by means of an accurate numerical analysis of the line … More arized Boltzmann equation. The mathematical proof of the existence and uniqueness of the solution of this problem was also given. The relationship among the parameters provides the boundary condition for the fluid-dynamic equations in the fluid-dynamic limit for the slow flows of the mixture of vapors around the condensed phases of arbitrary shape. In addition, it was shown that, in the actual half-space problem, the nonlinearity becomes important even in the case of weak evaporation and condensation and changes the features of condensing flows dramatically from those of evaporating flows.3.By considering the fluid-dynamic limit of the Boltzmann equation, the ghost effect (the fact that the flows with infinitesimal speed have significant effects on the temperature field in this limit) was demonstrated in various physical situations. For example, the deformation of the temperature field caused by infinitesimal Benard convections in a gas between two parallel plates, the deformation of the temperature field caused by infinitesimal Taylor vortices in a gas between two cylinders at rest, and the deformation of partial pressures caused by infinitesimal evaporation and condensation in vapors at rest between two condensed phases have been clarified. Less

1.考虑了在有少量惰性气体存在的情况下，边界上有蒸发和凝结的蒸汽流动。通过考虑Boltzmann方程的流体动力学极限及其边界条件，系统地导出了描述这种流动的新型流体动力学。新的流体力学揭示了这样一个事实，即具有无穷小平均浓度的惰性气体的存在对总的蒸气流动有显著的影响。2.基于动力学理论，研究了二元混合蒸气从平面凝聚相蒸发并流向无穷远和相同的混合蒸气从无穷远流动并在平面凝聚相上冷凝（半空间问题）。首先，考虑了弱蒸发和凝结的情况。通过对该线的精确数值分析，阐明了蒸汽的流动和参数之间的关系（与冷凝相和无穷远处的蒸汽有关 ...更多信息玻尔兹曼方程给出了该问题解的存在唯一性的数学证明。参数之间的关系提供了流体动力学方程的边界条件，在流体动力学限制的蒸汽混合物周围的任意形状的冷凝相的缓慢流动。此外，在实际的半空间问题中，即使在弱蒸发和冷凝的情况下，非线性也变得很重要，并且显著地改变了冷凝流动的特征。3.通过考虑Boltzmann方程的流体动力学极限，在各种物理情况下证明了虚影效应（具有无穷小速度的流动在该极限下对温度场具有显著影响的事实）。例如，在两个平行板之间的气体中由无穷小的Benard对流引起的温度场的变形，在两个静止圆柱之间的气体中由无穷小的Taylor涡引起的温度场的变形，以及在两个冷凝相之间的静止蒸汽中由无穷小的蒸发和冷凝引起的分压的变形已经被阐明。少