Boundary layer stability in real vanishing viscosity limit

In the previous paper [20], an Evans function machinery for the study of boundary layer stability was developed. There, the analysis was restricted to strongly parabolic perturbations, that is to an approximation of the form u(t) + (F(u))(x) = upsilon (B(u)u(x))(x) (upsilon much less than 1) with an "elliptic" matrix B. However, real models, like the Navier-Stokes approximation of the Euler equations for a gas flow, involve incompletely parabolic perturbations: B is not invertible in general. We first adapt the Evans function to this realistic framework, assuming that the boundary is not characteristic, neither for the hyperbolic first order system u(t) + (F(u))(x) = 0, nor for the perturbed system. We then apply it to the various kinds of boundary layers for a gas flow. We exhibit some exam les of unstable boundary layers for a perfect gas, when the viscosity dominates heat conductivity.