Long-time stability of large-amplitude noncharacteristic boundary layers for hyperbolic-parabolic systems

Toan Nguyen, Kevin Zumbrun

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9 Scopus citations

Abstract

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 with inflow or outflow boundary conditions, 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.

Original languageEnglish (US)
Pages (from-to)547-598
Number of pages52
JournalJournal des Mathematiques Pures et Appliquees
Volume92
Issue number6
DOIs
StatePublished - Dec 1 2009

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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