A new approach to the nonlinear stability of viscous flow in a coplanar magnetic field |
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| Authors: | Lanxi Xu Wanli Lan |
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| Institution: | College of Chemical Engineering, Department of Mathematics, Beijing University of Chemical Technology, Beijing, China |
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| Abstract: | 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(Re) and magnetic Reynolds numbers(Rm) below π2/2M. 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. |
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| Keywords: | plane parallel shear flow Lyapunov direct method Lyapunov function nonlinear stability Reynolds number magnetic Reynolds number |
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