Existence of nonlinear boundary layer solution to the Boltzmann equation with physical boundary conditions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:356

Article

Tian, Qianzhu^1,2,3,4 

[1] Univ Sci & Technol China, Joint Adv Res Ctr, Suzhou, Jiangsu, Peoples R China

[2] City Univ Hong Kong, Suzhou, Jiangsu, Peoples R China

[3] Univ Sci & Technol China, Dept Math, Hefei 230026, Anhui, Peoples R China

[4] City Univ Hong Kong, Dept Math, Kowloon, Hong Kong, Peoples R China

关键词: Boltzmann equation;    Diffuse reflection;    Specular reflection;    Boundary layer;   

DOI  :  10.1016/j.jmaa.2009.02.028

来源: Elsevier

【 摘 要 】

In this paper, the existence of boundary layer solutions to the Boltzmann equation with two physical boundary conditions for hard sphere model is considered. The boundary condition is first imposed on incoming particles of diffuse reflection type and the solution tends to a global Maxwellian in the far field. Similar to the problem with Dirichlet boundary condition studied in [S. Ukai, T. Yang, S.H. Yu, Nonlinear boundary layers of the Boltzmann equation: I. Existence, Comm. Math. Phys. 236 (3) (2003) 373-393], the existence of a solution is shown to depend on the Mach number of the far field Maxwellian, and there is an implicit solvability conditions yielding the co-dimensions of the boundary data. At last, the specular reflection boundary condition is considered and the similar conclusions are obtained. (C) 2009 Elsevier Inc. All rights reserved.

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