Boundary layer stability in real vanishing viscosity limit

In the previous paper [20], an Evans function machinery for the study of bo undary 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 approxim ation 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 tha t the boundary is not characteristic, neither for the hyperbolic first orde r 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.