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January  2009, 24(1): 145-157. doi: 10.3934/dcds.2009.24.145

Boltzmann equation, boundary effects

Tai-Ping Liu 1, and  Shih-Hsien Yu 2,

1. 

Institute of Mathematics, Academia Sinica, Taiwan
2. 

Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore 117543, Singapore

Received  December 2007 Revised  July 2008 Published  January 2009

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.
Keywords: boundary condition, Green's function, pointwise estimates., Boltzmann equation.
Mathematics Subject Classification: 76P05, 35L65, 82C4.
Citation: Tai-Ping Liu, Shih-Hsien Yu. Boltzmann equation, boundary effects. Discrete and Continuous Dynamical Systems, 2009, 24 (1) : 145-157. doi: 10.3934/dcds.2009.24.145
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