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