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**Slow rarefied flows. Theory and application to micro-electro-mechanical systems.**
*(English)*
Zbl 1097.82001

Progress in Mathematical Physics 41. Basel: Birkhäuser (ISBN 3-7643-7534-5/hbk). xi, 166 p. (2006).

The problems of slow rarefied gas flows are discussed in the seven chapters of this book. General results are based on the Boltzmann equation. The first four chapters review fundamental mathematical problems of the nonlinear Boltzmann equation. The Cauchy problem for the Boltzmann equation and the evolution of the particle distribution function of rarefied gases are discussed. Here the readers could find discussions of all basic problems: the main properties of the collision operator of the Boltzmann equation, problems of nonlinear Boltzmann equations, theorems on validity, existence and uniqueness of the Boltzmann equation and latest results on solutions of boundary value problems.

The last three chapters may be more interesting for scientists who are working on applications of rarefied gas flow to micro-electromechanic systems. The fifth chapter is devoted to the solution of the Boltzmann equation in a slab. The solution of the Poiseuille flow of rarefied gases is given in part 5.5. The last chapter is devoted to perspectives of using the Boltzmann equation for problems of rarefied lubrications in micro-electromechanic systems. Readers could find some comparisons of the microscopic results that are obtained from the kinetic theory with experiments.

This book is recommended for advanced graduate students and for scientists who are interested in mathematical problems of statistical mechanics, rarefied gas flow and micro- and nano-machines.

The last three chapters may be more interesting for scientists who are working on applications of rarefied gas flow to micro-electromechanic systems. The fifth chapter is devoted to the solution of the Boltzmann equation in a slab. The solution of the Poiseuille flow of rarefied gases is given in part 5.5. The last chapter is devoted to perspectives of using the Boltzmann equation for problems of rarefied lubrications in micro-electromechanic systems. Readers could find some comparisons of the microscopic results that are obtained from the kinetic theory with experiments.

This book is recommended for advanced graduate students and for scientists who are interested in mathematical problems of statistical mechanics, rarefied gas flow and micro- and nano-machines.

Reviewer: Oleg A. Sinkevich (Moskva)

### MSC:

82-02 | Research exposition (monographs, survey articles) pertaining to statistical mechanics |

82B40 | Kinetic theory of gases in equilibrium statistical mechanics |

82C40 | Kinetic theory of gases in time-dependent statistical mechanics |

82D99 | Applications of statistical mechanics to specific types of physical systems |

76P05 | Rarefied gas flows, Boltzmann equation in fluid mechanics |