具有表面张力和界面的三维赤道水波的liouville型结果

IF 1 3区数学 Q1 MATHEMATICS

Annali di Matematica Pura ed Applicata Pub Date : 2024-11-29 DOI:10.1007/s10231-024-01529-w

Yan Bai, Yong Zhang, Zhitao Zhang

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引用次数: 0

摘要

本文研究了赤道附近具有等涡度的地球物理分层水波的动力学问题。首先证明了f平面近似方程下三维无粘重力水波的有界解是二维的。建立了重力-毛细水波和带刚性盖重力水波有界解的二维特征。其次，我们重点研究了重力的刚性盖子情况和\(\beta \) -平面近似控制的重力-毛细层状水波。在这里，我们发现只有具有恒定涡量矢量的流动是具有平坦界面和消失速度场的静止流动。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Liouville-type results for three-dimensional equatorial water waves with surface tension and an interface

In this paper, we investigate the dynamics of geophysically stratified water waves with constant vorticity near the equator. Firstly, we prove that the bounded solutions of the three-dimensional inviscid gravity water wave governed by the f-plane approximation equation are two-dimensional. Moreover, we establish the two-dimensional characteristics of bounded solutions for gravity-capillary water waves and gravity water waves with rigid lids. Secondly, we focus on rigid lid case of gravity and gravity-capillary stratified water waves controlled by the \(\beta \)-plane approximation. Here, we find that the only flow with a constant vorticity vector is a stationary flow with a flat interface and a vanishing velocity field.

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来源期刊

Annali di Matematica Pura ed Applicata 数学-数学

CiteScore

2.10

自引率

10.00%

发文量

审稿时长

>12 weeks

期刊介绍： This journal, the oldest scientific periodical in Italy, was originally edited by Barnaba Tortolini and Francesco Brioschi and has appeared since 1850. Nowadays it is managed by a nonprofit organization, the Fondazione Annali di Matematica Pura ed Applicata, c.o. Dipartimento di Matematica "U. Dini", viale Morgagni 67A, 50134 Firenze, Italy, e-mail annali@math.unifi.it). A board of Italian university professors governs the Fondazione and appoints the editors of the journal, whose responsibility it is to supervise the refereeing process. The names of governors and editors appear on the front page of each issue. Their addresses appear in the title pages of each issue.