Boltzmann equation, boundary effects

Tai-Ping Liu; Shih-Hsien Yu

doi:10.3934/dcds.2009.24.145

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2009, Volume 24, Issue 1: 145-157. Doi: 10.3934/dcds.2009.24.145

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Boltzmann equation, boundary effects

Tai-Ping Liu^1, and
Shih-Hsien Yu^2,

1.
Institute of Mathematics, Academia Sinica
2.
Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore 117543

Received: November 30, 2007

Revised: June 30, 2008

Published: December 2008

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Abstract

The Boltzmann equation, [1], offers richer and physically more realistic modelling of the boundary effects than the fluid dynamic equations. Important phenomena such as the thermal transpiration and some of the bifurcations due to curvature of the boundary can only modeled using the kinetic formulation. In this paper we survey the analytical ideas that have been introduced in recent years for the study of the boundary effects. The main point is that more quantitative estimates of the solutions are needed for such a study.

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Mathematics Subject Classification: 76P05, 35L65, 82C40.

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