In this paper, we consider the nonlinear stability of a boundary layer of the Boltzmann equation with the cutoff hard potential when Mach number at far-field is greater than 1. Based on the Green’s function for the Cauchy problem constructed in M.-Y. Lee, T.-P. Liu and S.-H. Yu and the weighted energy method, we obtain the estimates for the Green’s function of the initial boundary problem and use it to obtain the nonlinear stability with an almost exponential convergent rate to the nonlinear Knudsen layer.
"Pointwise convergence of the boundary layer of the Boltzmann equation for the cutoff hard potential." Methods Appl. Anal. 14 (4) 307 - 344, December 2007.