© 2006

Slow Rarefied Flows

Theory and Application to Micro-Electro-Mechanical Systems

  • Provides an understanding of the essential mathematical tools required to deal with slow rarefied flows

  • Material can be used for a one-semester course or seminar

  • Gives the background for studies of the original literature

  • It is devised in such a way that certain parts can be skipped by readers interested in mathematical aspects and others by readers interested in applications.


Part of the Progress in Mathematical Physics book series (PMP, volume 41)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Pages 103-129
  3. Back Matter
    Pages 165-168

About this book


The book presents the mathematical tools used to deal with problems related to slow rarefied flows, with particular attention to basic concepts and problems which arise in the study of micro- and nanomachines. The mathematical theory of slow flows is presented in a practically complete fashion and provides a rigorous justification for the use of the linearized Boltzmann equation, which avoids costly simulations based on Monte Carlo methods. The book surveys the theorems on validity and existence, with particular concern for flows close to equilibria, and discusses recent applications of rarefied lubrication theory to micro-electro-mechanical systems (MEMS). It gives a general acquaintance of modern developments of rarefied gas dynamics in various regimes with particular attention to low speed microscale gas dynamics.

Senior students and graduates in applied mathematics, aerospace engineering, and mechanical mathematical physics will be provided with a basis for the study of molecular gas dynamics. The book will also be useful for scientific and technical researchers engaged in the research on gas flow in MEMS.


Boltzmann equation Boundary value problem Cauchy problem Flow Lubrification MEMS Monte Carlo method PDE Perturbation

Authors and affiliations

  1. 1.Dipartimento di MatematicaPolitecnico di MilanoMilanoItaly

Bibliographic information

Industry Sectors
Energy, Utilities & Environment


From the reviews: “The main topic of the book is rarefied gas dynamics which can be defined as the study of gas flows in which the distance between two subsequent collisions of a molecule … is not negligible in comparison with the length typical for the surrounding structure. … The book will be useful to specialists in the mathematical theory of fluids. It can serve also those who are beginners in this area provided they have some erudition in mathematics on graduate level.” (Ivan Straškraba, Applications of Mathematics, Vol. 54 (4), 2009)