<p> Lanford's theorem is the best known mathematical justification of Boltzmann's equation starting from deterministic classical mechanics. Unfortunately, Lanford's landmark result is only known to hold on a short time interval, whose size is comparable to the mean free time for a particle of gas. This limitation has only been overcome in restrictive perturbative regimes, most notably the case of an extremely rarefied gas of hard spheres in vacuum, which was studied by Illner and Pulvirenti in the 1980s. We give a complete proof of the convergence result due to Illner and Pulvirenti, building on the recent complete proof of Lanford's theorem by Gallagher, Saint-Raymond and Texier. Additionally, we introduce a notion that we call <i>nonuniform chaoticity </i> (classically known as strong one-sided chaos) which is propagated forwards in time under the microscopic dynamics, at least for the full time interval upon which uniform <i>L</i><sup>∞</sup> estimates are available for a specific ("tensorized'') solution of the BBGKY hierarchy. </p>
| Identifer | oai:union.ndltd.org:PROQUEST/oai:pqdtoai.proquest.com:10139568 |
| Date | 20 September 2016 |
| Creators | Denlinger, Ryan |
| Publisher | New York University |
| Source Sets | ProQuest.com |
| Language | English |
| Detected Language | English |
| Type | thesis |
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