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JNS

2010

2010

This paper introduces a new method to show the validity of a continuum description for the deterministic dynamics of many interacting particles. Here the many particle evolution is analyzed for a hard sphere ﬂow with the addition that after a collision the collided particles are removed from the system. We consider random initial conﬁgurations which are drawn from a Poisson point process with spatially homogeneous velocity density f0(v). Assuming that the moments of order less than three of f0 are ﬁnite and no mass is concentrated on lines, the homogeneous Boltzmann equation without gain term is derived for arbitrary long times in the Boltzmann-Grad scaling. A key element is a characterization of the many particle ﬂow by a hierarchy of trees which encode the possible collisions. The occurring trees are shown to have favorable properties with a high probability, allowing to restrict the analysis to a ﬁnite number of interacting particles, enabling us to extract a single-body d...

Added |
28 Jan 2011 |

Updated |
28 Jan 2011 |

Type |
Journal |

Year |
2010 |

Where |
JNS |

Authors |
Karsten Matthies, Florian Theil |

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