On Asymptotic Stability of Noncharacteristic Viscous Boundary Layers

We extend our recent work with K. Zumbrun on long-time stability of multidimensional noncharacteristic viscous boundary layers of a class of symmetrizable hyperbolicparabolic 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; (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.