On asymptotic stability of noncharacteristic viscous boundary layers

Details On asymptotic stability of noncharacteristic viscous boundary layers On asymptotic stability of noncharacteristic viscous boundary layers

2008-12-30

arxiv.org/abs/0812.5068v2

Mathematics

Analysis of PDEs

21 pages

Scientific paper

We extend our recent work with K. 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 $d\ge 2$, yielding the result for certain magnetohydrodynamics (MHD) layers; (ii) to drop a technical assumption on the so--called glancing set which was required in previous works. We also provide a different proof of low-frequency estimates by employing the method of Kreiss' symmetrizers, replacing the one relying on detailed derivation of pointwise bounds on the resolvent kernel.

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