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Hydrodynamic Limits of the Boltzmann Equation

  • Book
  • © 2009

Overview

Authors:
  1. Laure Saint-Raymond
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1971)

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Table of contents (6 chapters)

  1. Front Matter

    Pages 1-10
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  2. Introduction

    • Laure Saint-Raymond
    Pages 1-11

  3. The Boltzmann equation and its formal hydrodynamic limits

    • Laure Saint-Raymond
    Pages 1-34

  4. Mathematical tools for the derivation of hydrodynamic limits

    • Laure Saint-Raymond
    Pages 1-32

  5. The incompressible Navier-Stokes limit

    • Laure Saint-Raymond
    Pages 1-42

  6. The incompressible Euler limit

    • Laure Saint-Raymond
    Pages 1-42

  7. The compressible Euler limit

    • Laure Saint-Raymond
    Pages 1-6

  8. Back Matter

    Pages 1-25
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Keywords

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.

Reviews

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)

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