On asymptotic stability of noncharacteristic viscous boundary layers

2008/12/30 by Toan Nguyen, Toan T. Nguyen, Nguyen, Toan · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations #math-ph #math.AP #math.MP

paper · pdf · doi:10.48550/arxiv.0812.5068

21 pages

arxiv created 2008/12/31 · arxiv updated 2009/12/01

Abstract

We extend our recent work with K. Zumbrun on long-time stability of multi-dimensional noncharacteristic viscous boundary layers of a class of symmetrizable hyperbolic-parabolic systems. Our main improvements are (i) to establish the stability for a larger class of systems in dimensions d≥ 2, yielding the result for certain magnetohydrodynamics (MHD) layers; (ii) to drop a technical assumption on the so--called glancing set which was required in previous works. We also provide a different proof of low-frequency estimates by employing the method of Kreiss' symmetrizers, replacing the one relying on detailed derivation of pointwise bounds on the resolvent kernel.

Citations

• Stability of noncharacteristic boundary layers in the standing shock limit

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• Asymptotic behavior toward viscous shocks for the outflow problem of barotropic Navier-Stokes equations

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