### Abstract

This survey is a study of a dynamical system consisting of a massive piston in a cubic container of large size L filled with an ideal gas. The piston has mass M ∼ L^{2} and undergoes elastic collisions with N ∼ L^{3} non-interacting gas particles of mass m = 1. It is found that under suitable initial conditions there is a scaling regime with time and space scaled by L in which the motion of the piston and the one-particle distribution of the gas satisfy autonomous coupled equations (hydrodynamic equations) such that in the limit L → ∞ the mechanical trajectory of the piston converges in probability to the solution of the hydrodynamic equations for a certain period of time. There is also a heuristic discussion of the dynamics of the system on longer intervals of time.

Original language | English (US) |
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Pages (from-to) | 1045-1125 |

Number of pages | 81 |

Journal | Russian Mathematical Surveys |

Volume | 57 |

Issue number | 6 |

DOIs | |

State | Published - Jan 1 2002 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

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## Cite this

*Russian Mathematical Surveys*,

*57*(6), 1045-1125. https://doi.org/10.1070/RM2002v057n06ABEH000572