Nguyen, Toan On asymptotic stability of noncharacteristic viscous boundary layers. (English) Zbl 1211.35049 SIAM J. Math. Anal. 42, No. 3, 1156-1178 (2010). Summary: We extend our recent work with Kevin 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 \(d\geq2\), 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. Cited in 1 Document MSC: 35B40 Asymptotic behavior of solutions to PDEs 35L60 First-order nonlinear hyperbolic equations 35B35 Stability in context of PDEs Keywords:Kreiss symmetrizers; noncharacteristic boundary layers; asymptotic stability; glancing set; low-frequency estimates PDFBibTeX XMLCite \textit{T. Nguyen}, SIAM J. Math. Anal. 42, No. 3, 1156--1178 (2010; Zbl 1211.35049) Full Text: DOI arXiv