Provides a comprehensive description of the connections between kinetic theory and fluid dynamics. Presented are applications and models of physical problems such as flows induced by temperature fields, evaporation and condensation problems, examples of the ghost effect, and bifurcation of flows. The presentation is geared toward theoretical physicists, applied mathematicians, and engineers; thus, the monograph serves as a bridge for those working in different communities where kinetic theory is important. Classroom text for graduate students, or self-study resource for researchers and practitioners.

Includes supplementary material: sn.pub/extras

Inhalt
1 Introduction.- 2 Boltzmann Equation.- 2.1 Velocity distribution function and macroscopic variables.- 2.2 Boltzmann equation.- 2.3 Conservation equations.- 2.4 Maxwell distribution (Equilibrium distribution).- 2.5 Mean free path.- 2.6 Boundary condition.- 2.7 H theorem.- 2.8 Model equation.- 2.9 Nondimensional expressions I.- 2.10 Nondimensional expressions II.- 2.11 Linearized Boltzmann equation.- 2.12 Boltzmann equation in the cylindrical and spherical coordinate systems.- 3 Linear Theory Small Reynolds Numbers.- 3.1 Problem.- 3.2 GradHilbert solution and fluid-dynamic-type equations.- 3.3 Stress tensor and heat-flow vector of the GradHilbert solution.- 3.4 Analysis of the Knudsen layer.- 3.5 Slip condition and Knudsen-layer correction.- 3.6 Determination of macroscopic variables.- 3.7 Discontinuity of the velocity distribution function and S layer..- 3.8 Force and mass and energy transfers on a closed body.- 3.9 Viscosity and thermal conductivity.- 3.10 Summary of the asymptotic theory.- 3.11 Applications.- 4 Weakly Nonlinear Theory Finite Reynolds Numbers.- 4.1 Problem.- 4.2 S solution.- 4.3 Fluid-dynamic-type equations.- 4.4 Knudsen-layer analysis.- 4.5 Slip condition and Knudsen layer.- 4.6 Determination of macroscopic variables.- 4.7 Rarefaction effect.- 4.8 Force and mass and energy transfers on a closed body.- 4.9 Summary of the asymptotic theory and a comment on a time-dependent problem.- 4.10 Applications.- 5 Nonlinear Theory I Finite Temperature Variations and Ghost Effect.- 5.1 Problem.- 5.2 SB solution.- 5.3 Fluid-dynamic-type equations.- 5.4 Knudsen layer and slip condition.- 5.5 Determination of macroscopic variables.- 5.6 Ghost effect: Incompleteness of the system of the classical gas dynamics.- 5.7 Half-space problem of evaporationand condensation.- 6 Nonlinear Theory II - Flow with a Finite Mach Number around a Simple Boundary.- 6.1 Problem.- 6.2 Hilbert solution.- 6.3 Viscous boundary-layer solution.- 6.4 Knudsen-layer solution and slip condition.- 6.5 Connection of Hilbert and viscous boundary-layer solutions..- 6.6 Recipe for construction of solution.- 6.7 Discussions.- 7 Nonlinear Theory III Finite Speed of Evaporation and Condensation.- 7.1 Problem.- 7.2 Hilbert solution.- 7.3 Knudsen layer.- 7.4 Half-space problem of evaporation and condensation.- 7.5 System of equations and boundary conditions in the continuum limit.- 7.6 Generalized kinetic boundary condition.- 7.7 Boundary-condition functions $$ h1 \left( {Mn } \right),h2 \left( {Mn } \right),Fs \left( {Mn ,\overline M t ,{T \mathord{\left/ {\vphantom {T {Tw }}} \right. \kern-\nulldelimiterspace} {Tw }}} \right) $$ and $$ Fb \left( {Mn ,\overline M t ,{T \mathord{\left/ {\vphantom {T {Tw }}} \right. \kern-\nulldelimiterspace} {Tw }}} \right) $$.- 7.8 Applications.- 8 Bifurcation of Cylindrical Couette Flow with Evaporation.- 8.1 Problem.- 8.2 Solution type I.- 8.3 Solution type II.- 8.4 Bifurcation diagram and transition solution.- 8.5 Discussions for the other parameter range.- 8.6 Concluding remark and supplementary comment.- A Supplementary Explanations and Formulas.- A.1 Formal derivation of the Boltzmann equation from the Liouville equation.- A.3 Derivation of the Stokes set of equations.- A.4 Golse's theorem on a one-way flow.- A.6 Viscosity and thermal conductivity.- A.9 Equation for the Knudsen layer and Bardos's theorem.- A.10 The boundary condition for the linearized Euler set of equations.- B Spherically Symmetric Field of Symmetric Tensor.- B.1 Problem.- B.3.1 Preparation.- B.3.3 Summary.- B.4Applications.- B.4.2 Axially symmetric field.- C Kinetic-Equation Approach to Fluid-Dynamic Equations.- C.1 Introduction.- C.2 Exact kinetic-equation approach.- C.3 Discussion on numerical systems.