Stationary solutions to the exterior problems for the Boltzmann equation, I. Existence

Tong Yang; Seiji Ukai; Huijiang Zhao

doi:10.3934/dcds.2009.23.495

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2009, Volume 23, Issue 1&2: 495-520. Doi: 10.3934/dcds.2009.23.495

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Stationary solutions to the exterior problems for the Boltzmann equation, I. Existence

1.
17-26 Iwasaki, Hodogaya, Yokohama 240-0015
2.
Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong
3.
School of Mathematics and Statistics, Wuhan University, Wuhan 430072

Received: November 30, 2007

Revised: April 30, 2008

Published: April 2009

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Abstract

The exterior problem arising from the study of a flow past anobstacle is one of the most classical and important subjects in gasdynamics and fluid mechanics. The point of this problem is to assignthe bulk velocity at infinity, which is not a trivial driving forceon the flow so that some non-trivial solution profiles persist. Inthis paper, we consider the exterior problem for the Boltzmannequation when the Mach number of the far field equilibrium state issmall. The result here generalizes the previous one by Ukai-Asano onthe same problem to more general boundary conditions by cruciallyusing the velocity average argument.

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Mathematics Subject Classification: Primary: 76P05; Secondary: 35F20; 76E30; 82C40.

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