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.
All Science Journal Classification (ASJC) codes
- Computational Mathematics
- Applied Mathematics