## About Kac's Program in Kinetic Theory

dc.contributor.author | Mischler, Stéphane | en |

dc.contributor.author | Mouhot, Clement Mouhot | en |

dc.date.accessioned | 2018-04-23T14:37:15Z | |

dc.date.available | 2018-04-23T14:37:15Z | |

dc.identifier.issn | 1631-073X | |

dc.identifier.uri | https://www.repository.cam.ac.uk/handle/1810/275127 | |

dc.description.abstract | In this Note we present the main results from the recent work arxiv:1107.3251, which answers several conjectures raised fifty years ago by Kac. There Kac introduced a many-particle stochastic process (now denoted as Kac's master equation) which, for chaotic data, converges to the spatially homogeneous Boltzmann equation. We answer the three following questions raised in \cite{kac}: (1) prove the propagation of chaos for realistic microscopic interactions (i.e. in our results: hard spheres and true Maxwell molecules); (2) relate the time scales of relaxation of the stochastic process and of the limit equation by obtaining rates independent of the number of particles; (3) prove the convergence of the many-particle entropy towards the Boltzmann entropy of the solution to the limit equation (microscopic justification of the $H$-theorem of Boltzmann in this context). These results crucially rely on a new theory of quantitative uniform in time estimates of propagation of chaos. | |

dc.subject | math.AP | en |

dc.subject | math.AP | en |

dc.subject | math-ph | en |

dc.subject | math.MP | en |

dc.subject | math.PR | en |

dc.title | About Kac's Program in Kinetic Theory | en |

dc.type | Article | |

prism.endingPage | 1250 | |

prism.publicationName | 2 | en |

prism.startingPage | 1245 | |

prism.volume | 4 | en |

dc.identifier.doi | 10.17863/CAM.22307 | |

rioxxterms.versionofrecord | 10.1016/j.crma.2011.11.012 | en |

rioxxterms.version | AM | * |

rioxxterms.licenseref.uri | http://www.rioxx.net/licenses/all-rights-reserved | en |

rioxxterms.type | Journal Article/Review | en |

dc.identifier.url | http://dx.doi.org/10.1016/j.crma.2011.11.012 | en |

rioxxterms.freetoread.startdate | 2012-12-01 |