Exterior Problem of Boltzmann Equation with Temperature Difference

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January 2009, 8(1): 473-491. doi: 10.3934/cpaa.2009.8.473

Exterior Problem of Boltzmann Equation with Temperature Difference

Seiji Ukai ^1, , Tong Yang ^2, 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

Received February 2008 Revised July 2008 Published October 2008

Abstract
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The existence of stationary solution to an exterior domain of the Boltzmann equation was first studied by S. Ukai and K. Asano in [25, 27] and was recently generalized by S. Ukai, T. Yang, and H. J. Zhao in [29] to more general boundary conditions. We note, however, that the results obtained in [25, 29] require that the temperature of the far field Maxwellian is the same as the one of the Maxwellian preserved by the boundary conditions. The main purpose of this paper is to discuss the case when these two temperatures are different. The analysis is based on some new estimates on the linearized collision operator and the method introduced in [25, 27, 29].

Keywords: exterior problem, stationary solutions, Boltzmann equation, temperature difference.

Mathematics Subject Classification: Primary: 82C40; Secondary: 35B30, 35Q35, 76P05.

Citation: Seiji Ukai, Tong Yang, Huijiang Zhao. Exterior Problem of Boltzmann Equation with Temperature Difference. Communications on Pure & Applied Analysis, 2009, 8 (1) : 473-491. doi: 10.3934/cpaa.2009.8.473

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