© 2009

Hydrodynamic Limits of the Boltzmann Equation


Part of the Lecture Notes in Mathematics book series (LNM, volume 1971)

Table of contents

  1. Front Matter
    Pages 1-10
  2. Laure Saint-Raymond
    Pages 1-11
  3. Laure Saint-Raymond
    Pages 1-42
  4. Laure Saint-Raymond
    Pages 1-42
  5. Laure Saint-Raymond
    Pages 1-6
  6. Back Matter
    Pages 1-25

About this book


The aim of this book is to present some mathematical results describing the transition from kinetic theory, and, more precisely, from the Boltzmann equation for perfect gases to hydrodynamics.
Different fluid asymptotics will be investigated, starting always from solutions of the Boltzmann equation which are only assumed to satisfy the estimates coming from physics, namely some bounds on mass, energy and entropy.


Boltzmann equation dynamics hydrodynamic limits moment method relative entropy method

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From the reviews:

“The problems of hydrodynamic limits for the Boltzmann equation are discussing in the six chapters book. General results are based on the Boltzmann equation and are considering the transition from kinetic theory to hydrodynamic equations. … This book may be useful for advanced graduate students and for scientists who are interesting on mathematical problems of the statistical mechanics and rarefied gases.” (Oleg A. Sinkevich, Zentralblatt MATH, Vol. 1171, 2009)

“The main topic of the book is the presentation of mathematical results for the hydrodynamic limits of the Boltzmann equation in the kinetic theory of gases. … The book concludes with appendix containing theorems and concepts which aid in the reading of the book. … The book is written in a clear comprehensive style with detailed proofs … . This book is accessible to researchers, lecturers and graduate students in the fields of applied mathematics, mathematical physics and fluid mechanics.”­­­ (Andrzej Icha, Pure and Applied Geophysics, Vol. 168, 2011)