We study the steady Boltzmann equation in half-space, which arises in the Knudsen boundary layer problem, with diffusive reflection boundary conditions. Under certain admissible conditions, we establish the existence of a boundary layer solution for both linear and nonlinear Boltzmann equations in half-space with diffusive reflection boundary condition in $L^\infty_{x,v}$ when the far-field Mach number of the Maxwellian is zero. The continuity and the spacial decay of the solution are obtained. The uniqueness is established under some constraint conditions.
Publication:
SIAM Journal on Mathematical Analysis. Volume. 54, Issue. 3, pp: 3480-3534.
Author:
Feimin Huang
Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100190, China, and School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
Email: fhuang@amt.ac.cn
Yong Wang
Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100190, China, and School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
Email: yongwang@amss.ac.cn
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