### Abstract

We investigate the dynamics of the gas bounded by an infinite flat plate which is initially in equilibrium and set at some instant impulsively into uniform motion in its own plane. We use the Boltzmann equation to describe intermolecular collisions and assume the diffuse reflection to describe the interaction of the gas with the boundary. The Mach number of the plate is assumed to be small so that we can linearize the Boltzmann equation as well as the boundary condition. We show that the asymptotic behavior of the gas represents a perturbation to the free molecular gas when the time is much less than the mean free time. On the other hand, if the time is much greater than the mean free time, we show that the gas dynamics is governed by the linearized Navier–Stokes equation with a slip flow on the boundary and establish a boundary layer correction with thickness of the order of the mean free path. We also establish the singularity of velocity distribution function along the particle trajectory near the boundary.

Original language | English |
---|---|

Pages (from-to) | 1247-1275 |

Number of pages | 29 |

Journal | Journal of Statistical Physics |

Volume | 166 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2017 Mar 1 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

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*Journal of Statistical Physics*, vol. 166, no. 5, pp. 1247-1275. https://doi.org/10.1007/s10955-017-1717-y

**Asymptotic Behavior for Rayleigh Problem Based on Kinetic Theory.** / Kuo, Hung Wen.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Asymptotic Behavior for Rayleigh Problem Based on Kinetic Theory

AU - Kuo, Hung Wen

PY - 2017/3/1

Y1 - 2017/3/1

N2 - We investigate the dynamics of the gas bounded by an infinite flat plate which is initially in equilibrium and set at some instant impulsively into uniform motion in its own plane. We use the Boltzmann equation to describe intermolecular collisions and assume the diffuse reflection to describe the interaction of the gas with the boundary. The Mach number of the plate is assumed to be small so that we can linearize the Boltzmann equation as well as the boundary condition. We show that the asymptotic behavior of the gas represents a perturbation to the free molecular gas when the time is much less than the mean free time. On the other hand, if the time is much greater than the mean free time, we show that the gas dynamics is governed by the linearized Navier–Stokes equation with a slip flow on the boundary and establish a boundary layer correction with thickness of the order of the mean free path. We also establish the singularity of velocity distribution function along the particle trajectory near the boundary.

AB - We investigate the dynamics of the gas bounded by an infinite flat plate which is initially in equilibrium and set at some instant impulsively into uniform motion in its own plane. We use the Boltzmann equation to describe intermolecular collisions and assume the diffuse reflection to describe the interaction of the gas with the boundary. The Mach number of the plate is assumed to be small so that we can linearize the Boltzmann equation as well as the boundary condition. We show that the asymptotic behavior of the gas represents a perturbation to the free molecular gas when the time is much less than the mean free time. On the other hand, if the time is much greater than the mean free time, we show that the gas dynamics is governed by the linearized Navier–Stokes equation with a slip flow on the boundary and establish a boundary layer correction with thickness of the order of the mean free path. We also establish the singularity of velocity distribution function along the particle trajectory near the boundary.

UR - http://www.scopus.com/inward/record.url?scp=85009766184&partnerID=8YFLogxK

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U2 - 10.1007/s10955-017-1717-y

DO - 10.1007/s10955-017-1717-y

M3 - Article

AN - SCOPUS:85009766184

VL - 166

SP - 1247

EP - 1275

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 5

ER -