A new approach to the nonlinear stability of viscous flow in a coplanar magnetic field

作者：Xu, Lanxi^*; Lan, Wanli

来源：Mathematical Methods in the Applied Sciences, 2017, 40(10): 3415-3423.

DOI：10.1002/mma.4233

• plane parallel shear flow
• Lyapunov direct method
• Lyapunov function
• nonlinear stability
• Reynolds number
• magnetic Reynolds number

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 (2)/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.

• 出版日期2017-7-15
• 单位北京化工大学