The Classification of Well-Posed Kinetic Boundary Layer for Hard Sphere Gas Mixtures

Abstract

The kinetic boundary layer for gas mixtures is described by a half space boundary value problem for the two-species steady Boltzmann equation with an incoming distribution. We consider it around a drifting normalized bi-Maxwellian and prove that the boundary layer problem is well-posed when the drifting velocity u exceeds the sound speed , but one (respectively five, six) additional condition must be imposed when (respectively and ).