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

被引：1
|
作者：
Xu, Lanxi [1 ]
Lan, Wanli [1 ]
机构：
[1] Beijing Univ Chem Technol, Dept Math, Coll Chem Engn, Beijing 100029, Peoples R China
来源：
MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2017年 / 40卷 / 10期
关键词：
plane parallel shear flow; Lyapunov direct method; Lyapunov function; nonlinear stability; Reynolds number; magnetic Reynolds number; BENARD-PROBLEM;
D O I：
10.1002/mma.4233
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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. Copyright (c) 2016 John Wiley & Sons, Ltd.
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页码：3415 / 3423
页数：9
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