On asymptotic stability of noncharacteristic viscous boundary layers

Research output: Contribution to journalArticle

Abstract

We extend our recent work with Kevin Zumb run on long-time stability of multidimensional 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, and (ii) to drop a technical assumption on the so-called glancing set which was used in previous works. We also provide a different proof of low-frequency estimates by employing the method of Kreiss' symmetrizers, giving an alternative to the previous one relying on detailed derivation of pointwise bounds on the resolvent kernel.

Original languageEnglish (US)
Pages (from-to)1156-1178
Number of pages23
JournalSIAM Journal on Mathematical Analysis
Volume42
Issue number3
DOIs
StatePublished - Jun 18 2010

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Asymptotic stability
Asymptotic Stability
Boundary Layer
Boundary layers
Parabolic Systems
Hyperbolic Systems
Magnetohydrodynamics
Resolvent
Low Frequency
kernel
Alternatives
Estimate
Class

All Science Journal Classification (ASJC) codes

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

Cite this

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On asymptotic stability of noncharacteristic viscous boundary layers. / Nguyen, Toan.

In: SIAM Journal on Mathematical Analysis, Vol. 42, No. 3, 18.06.2010, p. 1156-1178.

Research output: Contribution to journalArticle

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