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On inhibition of the Rayleigh–Taylor instability by a horizontal magnetic field in ideal MHD fluids with velocity damping.

Authors :
Jiang, Fei
Jiang, Song
Zhao, Youyi
Source :
Journal of Differential Equations. Mar2022, Vol. 314, p574-652. 79p.
Publication Year :
2022

Abstract

It is still open whether the inhibition phenomenon of the Rayleigh–Taylor (RT) instability by a horizontal magnetic field can be mathematically verified for a non-resistive magnetohydrodynamic (MHD) fluid in a two-dimensional (2D) horizontal slab domain, since it was roughly verified in the linearized case by Wang in [43]. In this paper, we show that this inhibition phenomenon can be rigorously verified in the (nonlinear) inhomogeneous, incompressible, inviscid case with velocity damping. More precisely, we show that there is a critical number m C , such that if the strength | m | of a horizontal magnetic field is bigger than m C , then the small perturbation solution around the magnetic RT equilibrium state is exponentially stable in time. Moreover, we also provide a nonlinear instability result for the case | m | ∈ (0 , m C). Our instability result reveals that a horizontal magnetic field can not inhibit the RT instability, if it's strength is too small. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
00220396
Volume :
314
Database :
Academic Search Index
Journal :
Journal of Differential Equations
Publication Type :
Academic Journal
Accession number :
154995410
Full Text :
https://doi.org/10.1016/j.jde.2022.01.013