## Kinetic Theory and Fluid DynamicsThis monograph is intended to provide a comprehensive description of the rela tion between kinetic theory and fluid dynamics for a time-independent behavior of a gas in a general domain. A gas in a steady (or time-independent) state in a general domain is considered, and its asymptotic behavior for small Knudsen numbers is studied on the basis of kinetic theory. Fluid-dynamic-type equations and their associated boundary conditions, together with their Knudsen-layer corrections, describing the asymptotic behavior of the gas for small Knudsen numbers are presented. In addition, various interesting physical phenomena derived from the asymptotic theory are explained. The background of the asymptotic studies is explained in Chapter 1, accord ing to which the fluid-dynamic-type equations that describe the behavior of a gas in the continuum limit are to be studied carefully. Their detailed studies depending on physical situations are treated in the following chapters. What is striking is that the classical gas dynamic system is incomplete to describe the behavior of a gas in the continuum limit (or in the limit that the mean free path of the gas molecules vanishes). Thanks to the asymptotic theory, problems for a slightly rarefied gas can be treated with the same ease as the corresponding classical fluid-dynamic problems. In a rarefied gas, a temperature field is di rectly related to a gas flow, and there are various interesting phenomena which cannot be found in a gas in the continuum limit. |

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### Contents

II | 1 |

III | 5 |

IV | 7 |

V | 8 |

VI | 9 |

VII | 10 |

VIII | 11 |

IX | 13 |

LVI | 152 |

LVII | 153 |

LVIII | 157 |

LIX | 160 |

LX | 167 |

LXI | 168 |

LXII | 173 |

LXIII | 185 |

X | 14 |

XI | 15 |

XII | 19 |

XIII | 24 |

XIV | 26 |

XV | 27 |

XVI | 28 |

XVII | 32 |

XVIII | 35 |

XIX | 44 |

XXI | 49 |

XXII | 52 |

XXIII | 53 |

XXIV | 57 |

XXV | 59 |

XXVI | 60 |

XXVIII | 63 |

XXIX | 64 |

XXX | 65 |

XXXI | 70 |

XXXII | 72 |

XXXIII | 81 |

XXXIV | 85 |

XXXV | 86 |

XXXVII | 92 |

XXXVIII | 97 |

XXXIX | 101 |

XL | 102 |

XLI | 103 |

XLII | 104 |

XLIII | 106 |

XLV | 109 |

XLVI | 113 |

XLVII | 116 |

XLVIII | 119 |

XLIX | 123 |

L | 125 |

LI | 135 |

LII | 137 |

LIII | 146 |

LIV | 148 |

LV | 151 |

LXIV | 192 |

LXV | 194 |

LXVI | 196 |

LXVII | 203 |

LXVIII | 204 |

LXIX | 206 |

LXX | 209 |

LXXI | 213 |

LXXII | 216 |

LXXIII | 220 |

LXXIV | 225 |

LXXV | 226 |

LXXVI | 231 |

LXXVII | 235 |

LXXVIII | 237 |

LXXIX | 242 |

LXXX | 244 |

LXXXI | 250 |

LXXXII | 253 |

LXXXIV | 257 |

LXXXV | 269 |

LXXXVI | 271 |

LXXXVII | 280 |

LXXXVIII | 285 |

LXXXIX | 289 |

XC | 292 |

XCI | 295 |

XCII | 297 |

XCIII | 298 |

XCIV | 301 |

XCV | 302 |

XCVI | 304 |

XCVII | 306 |

XCVIII | 311 |

XCIX | 312 |

CI | 313 |

CII | 315 |

CIII | 316 |

CIV | 324 |

327 | |

345 | |

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### Common terms and phrases

analysis Appendix asymptotic analysis asymptotic theory behavior Bifurcation diagram BKW equation BKW model Boltzmann equation boundary condition boundary-layer boundary-value problem Chapter classical gas dynamics coefficients collision integral complete condensation condition component function condensed phase continuum limit corresponding cylinder density derived determined diffuse reflection discussion Euler set expansion expressed finite fluid-dynamic fluid-dynamic-type equations Footnote formulas Golse Grad-Hilbert half-space half-space problem hard-sphere gas Hilbert solution incompressible infinity inhomogeneous term integral equation kinetic Knudsen-layer correction layer Mach number macroscopic variables Maxwellian mean free path molecular molecules Navier-Stokes set nondimensional nonlinear obtained parameters particle pipe poo/pw pressure PSBO quantities relation Reynolds number right-hand side satisfy set of equations simple boundary slip condition small Knudsen numbers solvability condition Sone Sone & Aoki Stokes set subscript Sugimoto symmetric T/TW Takata temperature field temperature gradient thermal conductivity thermal creep flow thermal-stress TSBO uniform velocity distribution function viSBi viscous