Exterior Problem of Boltzmann Equation with Temperature Difference

Pages: 473 - 491, Volume 8, Issue 1, January 2009

doi:10.3934/cpaa.2009.8.473       Abstract        Full Text (266.3K)       Related Articles

Seiji Ukai - 17-26 Iwasaki, Hodogaya, Yokohama 240-0015, Japan (email)
Tong Yang - Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong, China (email)
Huijiang Zhao - School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China (email)

Abstract: 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:  Boltzmann equation, exterior problem, stationary solutions, temperature difference
Mathematics Subject Classification:  Primary: 82C40; Secondary: 35B30, 35Q35, 76P05

Received: February 2008;      Revised: July 2008;      Published: October 2008.