Global-in-$x$ stability of Prandtl layer expansions for steady magnetohydrodynamics flows over a moving plate

Abstract

In this paper, we obtain the global-in-$x$ Sobolev stability of Prandtl layer expansions for 2-D steady incompressible MHD flows with shear outer ideal MHD flows $(1,0,\sigma ,0)$ ($\sigma \ge 0$) on a moving plate. It is worth noticing that in the Sobolev sense, the degeneracy of the tangential magnetic field in our result is allowed, which is much different from both the unsteady case in [25,26,27] and the steady case in [3,4].

arXiv commentSome typos are corrected

References in corpus (5)

• Gevrey Stability of Prandtl Expansions for 2D Navier-Stokes
• Sobolev stability of Prandtl expansions for the steady Navier-Stokes equations
• Global-in-$x$ Stability of Steady Prandtl Expansions for 2D Navier-Stokes Flows
• Boundary layer for 3D plane parallel channel flows of nonhomogeneous incompressible Navier-Stokes equations
• Boundary Layer Expansions for the Stationary Navier-Stokes Equations