2008/04/08 by Toan Nguyen, Toan T. Nguyen, Nguyen, Toan +2 · 2 citations
Engineering · Mathematics · #35B35 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Navier-Stokes equation solutions #math.AP #msc:35B35
paper · pdf · doi:10.48550/arxiv.0804.1345
arxiv created 2008/04/08 · openalex publication_date 2008/04/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Extending investigations of Yarahmadian and Zumbrun in the strictly parabolic case, we study time-asymptotic stability of arbitrary (possibly large) amplitude noncharacteristic boundary layers of a class of hyperbolic-parabolic systems including the Navier--Stokes equations of compressible gas- and magnetohydrodynamics, establishing that linear and nonlinear stability are both equivalent to an Evans function, or generalized spectral stability, condition. The latter is readily checkable numerically, and analytically verifiable in certain favorable cases; in particular, it has been shown by Costanzino, Humpherys, Nguyen, and Zumbrun to hold for sufficiently large-amplitude layers for isentropic ideal gas dynamics, with general adiabiatic index γ≥ 1. Together with these previous results, our results thus give nonlinear stability of large-amplitude isentropic boundary layers, the first such result for compressive (``shock-type'') layers in other than the nearly-constant case. The analysis, as in the strictly parabolic case, proceeds by derivation of detailed pointwise Green function bounds, with substantial new technical difficulties associated with the more singular, hyperbolic behavior in the high-frequency/short time regime.