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Abstract:
We investigate the nonlinear instability of a smooth Rayleigh Taylor steady-state solution (including the case of heavier density with increasing height) to the three-dimensional incompressible nonhomogeneous magneto hydrodynamic (MHD) equations of zero resistivity in the presence of a uniform gravitational field. We first analyze the linearized equations around the steadystate solution. Then we construct solutions of the linearized problem that grow in time in the Sobolev space H-k, thus leading to the linear instability. With the help of the constructed unstable solutions of the linearized problem and a local well-posedness result of smooth solutions to the original nonlinear problem, we establish the instability of the density, the horizontal and vertical velocities in the nonlinear problem. Moreover, when the steady magnetic field is vertical and small, we prove the instability of the magnetic field. This verifies the physical phenomenon: instability of the velocity leads to the instability of the magnetic field through the induction equation.
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Source :
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S
ISSN: 1937-1632
Year: 2016
Issue: 6
Volume: 9
Page: 1853-1898
0 . 7 8 1
JCR@2016
1 . 3 0 0
JCR@2023
ESI Discipline: MATHEMATICS;
ESI HC Threshold:76
JCR Journal Grade:3
CAS Journal Grade:4
Cited Count:
WoS CC Cited Count: 35
SCOPUS Cited Count: 36
ESI Highly Cited Papers on the List: 0 Unfold All
WanFang Cited Count:
Chinese Cited Count:
30 Days PV: 2
Affiliated Colleges: