Abstract:
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 =ν(B(u)u x ) x $ (ν≪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 examples of unstable boundary layers for a perfect gas, when the viscosity dominates heat conductivity.
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Received: 27 November 2000/ Accepted: 16 March 2001
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Serre, D., Zumbrun, K. Boundary Layer Stability¶in Real Vanishing Viscosity Limit. Commun. Math. Phys. 221, 267–292 (2001). https://doi.org/10.1007/s002200100486
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DOI: https://doi.org/10.1007/s002200100486