BIFURCATION OF ROTATING PATCHES FROM KIRCHHOFF VORTICES

被引：45

作者：

Hmidi, Taoufik ^{[1
]}

Mateu, Joan ^{[2
]}

机构：

[1] Univ Rennes 1, IRMAR, Campus Beaulieu, F-35042 Rennes, France

[2] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Catalonia, Spain

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2016年 / 36卷 / 10期

关键词：

Kirchhoff vortices; rotating patches; bifurcation; STEADY-STATE SOLUTIONS; EULER EQUATIONS; 2; DIMENSIONS; V-STATES; VORTEX; CONFIGURATIONS; REGULARITY; STABILITY; DYNAMICS; WAVES;

D O I：

10.3934/dcds.2016038

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we investigate the existence of a new family of rotating patches for the planar Euler equations. We shall prove the existence of countable branches bifurcating from the ellipses at some implicit angular velocities. The proof uses bifurcation tools combined with the explicit parametrization of the ellipse through the exterior conformal mappings. The boundary is shown to belong to Holderian class.

引用

页码：5401 / 5422

页数：22

共 50 条

[21] Chaos and bifurcation in nonlinear in-extensional rotating shafts [J].

Hosseini, S. A. A. .

SCIENTIA IRANICA, 2019, 26 (02) :856-868

[22] Spirals vortices in Taylor-Couette flow with rotating endwalls [J].

Heise, M. ;

Hochstrate, K. ;

Abshagen, J. ;

Pfister, G. .

PHYSICAL REVIEW E, 2009, 80 (04)

[23] Boundary Regularity of Rotating Vortex Patches [J].

Hmidi, Taoufik ;

Mateu, Joan ;

Verdera, Joan .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2013, 209 (01) :171-208

[24] The lowest stability and bifurcation in supercritical Taylor vortices [J].

Lin, Hau-Chieh ;

Chen, Bi-Chu ;

Chen, Yi-Fen .

INTERNATIONAL JOURNAL OF COMPUTATIONAL FLUID DYNAMICS, 2010, 24 (06) :227-233

[25] Global bifurcation of positive solutions for discrete Kirchhoff equations [J].

Shi, Xuanrong ;

Lei, Xiangbing .

DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL, 2025,

[26] Vortices and collective excitations in rotating BECs [J].

Wilkin, NK ;

Gunn, JMF .

PHYSICA B, 2000, 284 :23-24

[27] Local vortices in a differentially rotating flow [J].

V. A. Antonov ;

A. S. Baranov ;

B. P. Kondrat’ev .

Fluid Dynamics, 2005, 40 :71-82

[28] Uniformly rotating vortices for the lake equation [J].

Hmidi, Taoufik ;

Houamed, Haroune ;

Roulley, Emeric ;

Zerguine, Mohamed .

MATHEMATISCHE ANNALEN, 2025, 392 (03) :3065-3160

[29] Local Vortices in a Differentially Rotating Flow [J].

Antonov, V. A. ;

Baranov, A. S. ;

Kondrat'ev, B. P. .

FLUID DYNAMICS, 2005, 40 (01) :71-82

[30] Vortices in Rotating Gravitating Gas Disks [J].

Abrahamyan, M. G. .

ASTROPHYSICS, 2015, 58 (01) :89-105

← 1 2 3 4 5 →