Validity of Prandtl layer expansions for steady magnetohydrodynamics over a rotating disk

Abstract

This paper is concerned with the validity of Prandtl boundary layer expansions for 2D steady viscous incompressible magnetohydrodynamic (MHD) flows over a rotating disk {(θ, r) ∈ [0, θ0] × [R0, ∞)} with a moving curved boundary {r = R0}. We establish the validity of boundary layer expansions and convergence rates in the Sobolev sense. Then, we extend the results by Iyer [Arch. Ration. Mech. Anal. 224(2), 421–469 (2017)] for Navier–Stokes equations to the MHD flows.