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January & February  2009, 23(1&2): 495-520. doi: 10.3934/dcds.2009.23.495

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

Tong Yang 2, , Seiji Ukai 1, and  Huijiang Zhao 3,

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, China

Received  December 2007 Revised  May 2008 Published  September 2008

The exterior problem arising from the study of a flow past an obstacle is one of the most classical and important subjects in gas dynamics and fluid mechanics. The point of this problem is to assign the bulk velocity at infinity, which is not a trivial driving force on the flow so that some non-trivial solution profiles persist. In this paper, we consider the exterior problem for the Boltzmann equation when the Mach number of the far field equilibrium state is small. The result here generalizes the previous one by Ukai-Asano on the same problem to more general boundary conditions by crucially using the velocity average argument.
Keywords: stationary solutions, velocity average argument, Boltzmann equation, exterior problems.
Mathematics Subject Classification: Primary: 76P05; Secondary: 35F20; 76E30; 82C40.
Citation: Tong Yang, Seiji Ukai, Huijiang Zhao. Stationary solutions to the exterior problems for the Boltzmann equation, I. Existence. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 495-520. doi: 10.3934/dcds.2009.23.495
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