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A new approach to the nonlinear stability of viscous flow in a coplanar magnetic field
Author(s) -
Xu Lanxi,
Lan Wanli
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4233
Subject(s) - mathematics , laminar flow , magnetic field , reynolds number , nonlinear system , mathematical analysis , lyapunov function , stability (learning theory) , mechanics , physics , turbulence , quantum mechanics , machine learning , computer science
We present a new Lyapunov function for laminar flow, in the x ‐direction, between two parallel planes in the presence of a coplanar magnetic field for three‐dimensional perturbations with stress‐free boundary planes that provides conditional nonlinear stability for all Reynolds numbers( R e ) and magnetic Reynolds numbers( R m ) below π 2 /2 M . Compared with previous results on the nonlinear stability of this problem, the radius of stability ball and the energy decay rate obtained in this paper are independent of the magnetic field. Copyright © 2016 John Wiley & Sons, Ltd.