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

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dc.creatorNguyen, Toan
dc.creatorZumbrun, Kevin
dc.date2008-04-08
dc.date.accessioned2026-07-07T09:31:07Z
dc.date.available2026-07-07T09:31:07Z
dc.descriptionExtending 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 $γ\ge 1$. 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.
dc.identifierhttps://arxiv.org/abs/0804.1345
dc.identifierhttp://arxiv.org/abs/0804.1345
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/158347
dc.subjectAnalysis of PDEs
dc.subject35B35
dc.titleLong-time stability of large-amplitude noncharacteristic boundary layers for hyperbolic--parabolic systems
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