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On asymptotic stability of noncharacteristic viscous boundary layers. (English) Zbl 1211.35049

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.

MSC:

35B40 Asymptotic behavior of solutions to PDEs
35L60 First-order nonlinear hyperbolic equations
35B35 Stability in context of PDEs
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