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

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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