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From Newton to Boltzmann: Hard Spheres and Short-range Potentials

Isabelle Gallagher, Laure Saint-Raymond, and Benjamin Texier
Publisher: 
European Mathematical Society
Publication Date: 
2014
Number of Pages: 
135
Format: 
Paperback
Series: 
Zürich Lectures in Advanced Mathematics 18
Price: 
38.00
ISBN: 
9783037191293
Category: 
Monograph
We do not plan to review this book.

I. Introduction

  • The low density limit
  • The Boltzmann equation
  • Main results

II. The case of hard spheres

  • Microscopic dynamics and BBGKY hierarchy
  • Uniform a priori estimates for the BBGKY and Boltzmann hierarchies
  • Statement of the convergence result
  • Strategy of the proof of convergence

III. The case of short-range potentials

  • Two-particle interactions
  • Truncated marginals and the BBGKY hierarchy
  • Cluster estimates and uniform a priori estimates
  • Convergence result and strategy of proof

IV. Termwise convergence

  • Elimination of recollisions
  • Truncated collision integrals
  • Proof of convergence
  • Concluding remarks
  • Bibliography
  • Index

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