A note on the ill-posedness of shear flow for the MHD boundary layer equations
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review
Author(s)
Related Research Unit(s)
Detail(s)
Original language | English |
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Pages (from-to) | 2065-2078 |
Journal / Publication | Science China Mathematics |
Volume | 61 |
Issue number | 11 |
Online published | 23 Jul 2018 |
Publication status | Published - Nov 2018 |
Link(s)
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.
In: Science China Mathematics, Vol. 61, No. 11, 11.2018, p. 2065-2078.
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review