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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.

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Authors and Affiliations

  1. Department of Mathematics, Indiana University, Bloomington, IN, 47402, USA

    Toan Nguyen & Kevin Zumbrun

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  1. Toan Nguyen
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  2. Kevin Zumbrun
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Correspondence to Kevin Zumbrun.

Additional information

Communicated by P. Constantin

This work was supported in part by the National Science Foundation award number DMS-0300487.

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Nguyen, T., Zumbrun, K. Long-Time Stability of Multi-Dimensional Noncharacteristic Viscous Boundary Layers. Commun. Math. Phys. 299, 1–44 (2010). https://doi.org/10.1007/s00220-010-1095-7

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