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

2008/07/30 by Toan Nguyen, Nguyen, Toan, Kevin Zumbrun +1 · 1 citation
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.0807.4946

42 pp. Added comments to Appendix (only change)

arxiv created 2008/08/01 · arxiv updated 2009/12/01

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 stabiity 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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