A note on the ill-posedness of shear flow for the MHD boundary layer equations

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

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Detail(s)

Original languageEnglish
Pages (from-to)2065-2078
Journal / PublicationScience China Mathematics
Volume61
Issue number11
Online published23 Jul 2018
Publication statusPublished - Nov 2018

Abstract

For the two-dimensional Magnetohydrodynamics (MHD) boundary layer system, it has been shown that the non-degenerate tangential magneticfield leads to the well-posedness in Sobolev spaces and high Reynolds number limits without any monotonicity condition on the velocityfield in our previous works. This paper aims to show that suffcient degeneracy in the tangential magneticfield at a non-degenerate critical point of the tangential velocityfield of shear flow indeed yields instability as for the classical Prandtl equations without magneticfield studied by Gérard-Varet and Dormy (2010). This partially shows the necessity of the non-degeneracy in the tangential magneticfield for the stability of the boundary layer of MHD in 2D at least in Sobolev spaces.

Research Area(s)

  • ill-posedness, MHD boundary layer, Prandtl equations, shear flows, Sobolev spaces

Citation Format(s)

A note on the ill-posedness of shear flow for the MHD boundary layer equations. / Liu, Cheng-Jie; Xie, Feng; Yang, Tong.
In: Science China Mathematics, Vol. 61, No. 11, 11.2018, p. 2065-2078.

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review