## Abstract

A kinetic equation with a relaxation time model for wave-particle collisions is considered. Similarly to the BGK-model of gas dynamics, it involves a projection onto the set of equilibrium distributions, nonlinearly dependent on the moments of the distribution function. Under a diffusive and low Mach number scaling the macroscopic limit is a generalization of the incompressible Navier-Stokes equations, where the momentum equations are coupled to a diffusive equation for an energy distribution function. By a moment approximation, this system can be related to a low Mach number model of fluid mechanics, which already appeared in the literature. Finally, for a linearized version corresponding to Stokes flow an existence result for initial value problems is proved.

Original language | English (US) |
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Pages (from-to) | 179-194 |

Number of pages | 16 |

Journal | Journal of Statistical Physics |

Volume | 136 |

Issue number | 1 |

DOIs | |

State | Published - Jul 1 2009 |

## Keywords

- Cometary flows
- Diffusive scaling
- Kinetic equation
- Low Mach number model
- Macroscopic limit
- Wave-particle collision operator

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics