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Lecture Notes in Mathematics

Hydrodynamic Limits of the Boltzmann Equation

Authors: Saint-Raymond, Laure

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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)


Table of contents (6 chapters)

Table of contents (6 chapters)
  • Introduction

    Pages 1-11

    Saint-Raymond, Laure

  • The Boltzmann equation and its formal hydrodynamic limits

    Pages 1-34

    Saint-Raymond, Laure

  • Mathematical tools for the derivation of hydrodynamic limits

    Pages 1-32

    Saint-Raymond, Laure

  • The incompressible Navier-Stokes limit

    Pages 1-42

    Saint-Raymond, Laure

  • The incompressible Euler limit

    Pages 1-42

    Saint-Raymond, Laure

Buy this book

eBook $54.99
price for USA in USD
  • ISBN 978-3-540-92847-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $69.95
price for USA in USD
  • ISBN 978-3-540-92846-1
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually ready to be dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Hydrodynamic Limits of the Boltzmann Equation
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1971
Copyright
2009
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-92847-8
DOI
10.1007/978-3-540-92847-8
Softcover ISBN
978-3-540-92846-1
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XII, 194
Number of Illustrations
9 b/w illustrations
Topics

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