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Sharp nonlinear stability criterion of viscous non-resistive MHD internal waves in 3D. (arXiv:1602.02554v2 [math.AP] UPDATED)
来源于:arXiv
We consider the dynamics of two layers of incompressible electrically
conducting fluid interacting with the magnetic field, which are confined within
a 3D horizontally infinite slab and separated by a free internal interface. We
assume that the upper fluid is heavier than the lower fluid so that the fluids
are susceptible to the Rayleigh-Taylor instability. Yet, we show that the
viscous and non-resistive problem around the equilibrium is nonlinearly stable
provided that the strength of the vertical component of the steady magnetic
field, $|\bar B_3|$, is greater than the critical value, $\mathcal{M}_c$, which
we identify explicitly. We also prove that the problem is nonlinearly unstable
if $|\bar B_3|<\mathcal{M}_c$. Our results indicate that the non-horizontal
magnetic field has strong stabilizing effect on the Rayleigh-Taylor instability
but the horizontal one does not have in 3D. 查看全文>>