A classification of well‐posed kinetic layer problems

In the first part of this paper, we study the half space boundary value problem for the Boltzmann equation with an incoming distribution, obtained when considering the boundary layer arising in the kinetic theory of gases as the mean free path tends to zero. We linearize it about a drifting Maxwellian and prove that, as conjectured by Cercignani [4], the problem is well‐posed when the drift velocity u exceeds the sound speed c, but that one (respectively four, five) additional conditions must be imposed when 0 < u < c (respectively −c < u < 0 and u < −c). In the second part, we show that the well‐posedness and the asymptotic behavior results for kinetic layers equations with prescribed incoming flux can be extended to more general and realistic boundary conditions.