Entropy Methods for the Boltzmann Equation

Lectures from a Special Semester at the Centre Émile Borel, Institut H. Poincaré, Paris, 2001

  • Fraydoun Rezakhanlou
  • Cédric Villani
  • François Golse
  • Stefano Olla
Part of the Lecture Notes in Mathematics book series (LNM, volume 1916)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Back Matter
    Pages 107-111

About this book

Introduction

Entropy and entropy production have recently become mathematical tools for kinetic and hydrodynamic limits, when deriving the macroscopic behaviour of systems from the interaction dynamics of their many microscopic elementary constituents at the atomic or molecular level.

During a special semester on Hydrodynamic Limits at the Centre Émile Borel in Paris, 2001 two of the research courses were held by C. Villani and F. Rezakhanlou. Both illustrate the major role of entropy and entropy production in a mutual and complementary manner and have been written up and updated for joint publication. Villani describes the mathematical theory of convergence to equilibrium for the Boltzmann equation and its relation to various problems and fields, including information theory, logarithmic Sobolev inequalities and fluid mechanics. Rezakhanlou discusses four conjectures for the kinetic behaviour of the hard sphere models and formulates four stochastic variations of this model, also reviewing known results for these.

Keywords

Boltzmann equation H Theorem Stochastic Markov processes entropy interacting particle system kinetic limit

Authors and affiliations

  • Fraydoun Rezakhanlou
    • 1
  • Cédric Villani
    • 2
  1. 1.Department of Mathematics Evans HallUniversity of CaliforniaBerkeleyUSA
  2. 2.Unité de mathématiques pures et appliquées (UMR CNRS 5669)Ecole Normale Supérieure de LyonLyon Cedex 07France

Editors and affiliations

  • François Golse
    • 1
  • Stefano Olla
    • 2
  1. 1.Laboratoire Jacques-Louis Lions (UMR CNRS 7598)Université Pierre et Marie CurieParisFrance
  2. 2.Centre de recherche en mathématiques de la décision (UMR CNRS 7534)Université Paris - DauphineParis Cedex 16France

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-73705-6
  • Copyright Information Springer-Verlag Berlin Heidelberg 2008
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-73704-9
  • Online ISBN 978-3-540-73705-6
  • Series Print ISSN 0075-8434
  • About this book