Communications in Mathematical Physics

, Volume 299, Issue 1, pp 1–44 | Cite as

Long-Time Stability of Multi-Dimensional Noncharacteristic Viscous Boundary Layers

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Abstract

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 stability has been verified for small-amplitude layers by Guès, Métivier, 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.

Keywords

Boundary Layer Boundary Term Nonlinear Stability Evans Function Spectral Stability 
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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Department of MathematicsIndiana UniversityBloomingtonUSA

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