Steady periodic waves and formal stability for fixed-depth rotational equatorial flows

被引：16
作者：
Chu, Jifeng [1 ]
Ding, Qixing [1 ]
Yang, Yanjuan [2 ]
机构：
[1] Shanghai Normal Univ, Dept Math, Shanghai 200234, Peoples R China
[2] Hohai Univ, Dept Math, Nanjing 210098, Peoples R China
来源：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2020年 / 269卷 / 05期
基金：
中国国家自然科学基金;
关键词：
Steady periodic waves; Rotational equatorial flows; Fixed-depth; Dispersion relation; Formal stability; GRAVITY WATER-WAVES; DISPERSION-RELATIONS; VARIATIONAL FORMULATIONS; ANALYTICITY; PRINCIPLE; SYMMETRY;
D O I：
10.1016/j.jde.2020.03.040
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we apply the bifurcation theory to study the steady two-dimensional periodic equatorial water waves for the f-plane approximation. We consider the waves with vorticity which propagate with a specified fixed depth between the thermocline and the upper boundary of the centre layer. Moreover, we present a functional J and its first variation corresponds to the exact equations in the transformed variables. Using the second variation of J, we prove a formal stability result for the bifurcation inducing the laminar solution. (c) 2020 Elsevier Inc. All rights reserved.
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页码：4192 / 4214
页数：23
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