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

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,σ,0) (σ≥0) on a moving plate. It is worth noticing that in the Sobolev sense, the degeneracy of the tangential magnetic field in our re...

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Bibliographic Details
Published in:Journal of Differential Equations 2024-12, Vol.411, p.119-203
Main Authors: Ding, Shijin, Ji, Zhijun, Lin, Zhilin
Format: Article
Language:English
Subjects:
Boundary layer expansion
Incompressible MHD
Inviscid limit
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Summary: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,σ,0) (σ≥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 [25–27] and the steady case in [3,4].
ISSN:0022-0396
DOI:10.1016/j.jde.2024.08.019