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