Long-time stability of multi-dimensional noncharacteristic viscous boundary layers

Details Long-time stability of multi-dimensional noncharacteristic viscous boundary layers Long-time stability of multi-dimensional noncharacteristic viscous boundary layers

2008-07-30

arxiv.org/abs/0807.4946v2

Physics

Mathematical Physics

42 pp. Added comments to Appendix (only change)

Scientific paper

We establish long-time stability of multi-dimensional noncharacteristic boundary layers of a class of hyperbolic--parabolic systems including the compressible Navier--Stokes equations with inflow [outflow] boundary conditions, under the assumption of strong spectral, or uniform Evans, stability. Evans stabiity has been verified for small-amplitude layers by Gu\`es, M\'etivier, Williams, and Zumbrun. For large-amplitude layers, it may be efficiently checked numerically, as done in the one-dimensional case by Costanzino, Humpherys, Nguyen, and Zumbrun.

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