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

  • Isabelle Gallagher

    Université Paris-Diderot France
  • Laure Saint-Raymond

    Ecole Normale Superieure, France
  • Benjamin Texier

    Université Paris Diderot - Paris 7, France
From Newton to Boltzmann: Hard Spheres and Short-range Potentials cover

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FrontmatterDownload pp. i–iv
PrefaceDownload pp. v–vii
ContentsDownload pp. ix–xi
Part I Introductionp. 1
1The low density limitpp. 2–6
2The Boltzmann equationpp. 7–13
3Main resultspp. 14–18
Part II The case of hard spheresp. 19
4Microscopic dynamics and BBGKY hierarchypp. 20–29
5Uniform a priori estimates for the BBGKY and Boltzmann hierarchiespp. 30–38
6Statement of the convergence resultpp. 39–48
7Strategy of the proof of convergencepp. 49–56
Part III The case of short-range potentialsp. 57
8Two-particle interactionspp. 58–67
9Truncated marginals and the BBGKY hierarchypp. 68–80
10Cluster estimates and uniform a priori estimatespp. 81–90
11Convergence result and strategy of proofpp. 91–97
Part IV Termwise convergencep. 98
12Elimination of recollisionspp. 99–108
13Truncated collision integralspp. 109–116
14Proof of convergencepp. 117–127
15Concluding remarkspp. 128–129
Bibliographypp. 130–132
Notation Indexpp. 133–135
Indexp. 137

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