STEADY ASYMMETRIC VORTEX PAIRS FOR EULER EQUATIONS

被引：20
作者：
Hassainia, Zineb [1 ]
Hmidi, Taoufik [2 ]
机构：
[1] NYU, POB 129188, Abu Dhabi, U Arab Emirates
[2] Univ Rennes 1, IRMAR, Campus Beaulieu, F-35042 Rennes, France
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2021年 / 41卷 / 04期
关键词：
Euler equations; vortex dynamics; steady vortex pairs; desingularization; implicit function theorem; CONNECTED V-STATES; 2; DIMENSIONS; BIFURCATION; EXISTENCE; REGULARITY; PATCHES;
D O I：
10.3934/dcds.2020348
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we study the existence of co-rotating and counter-rotating unequal-sized pairs of simply connected patches for Euler equations. In particular, we prove the existence of curves of steadily co-rotating and counter-rotating asymmetric vortex pairs passing through a point vortex pairs with unequal circulations. We also provide a careful study of the asymptotic behavior for the angular velocity and the translating speed close to the point vortex pairs.
引用
收藏
页码：1939 / 1969
页数：31
相关论文
共 37 条
[1]   Periodic solutions with prescribed minimal period of vortex type problems in domains [J].
Bartsch, Thomas ;
Sacchet, Matteo .
NONLINEARITY, 2018, 31 (05) :2156-2172
[2]   MOTIONS OF VORTEX PATCHES [J].
BURBEA, J .
LETTERS IN MATHEMATICAL PHYSICS, 1982, 6 (01) :1-16
[3]   Uniformly Rotating Analytic Global Patch Solutions for Active Scalars [J].
Castro A. ;
Córdoba D. ;
Gómez-Serrano J. .
Annals of PDE, 2 (1)
[4]   Uniformly Rotating Smooth Solutions for the Incompressible 2D Euler Equations [J].
Castro, Angel ;
Cordoba, Diego ;
Gomez-Serrano, Javier .
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2019, 231 (02) :719-785
[5]   EXISTENCE AND REGULARITY OF ROTATING GLOBAL SOLUTIONS FOR THE GENERALIZED SURFACE QUASI-GEOSTROPHIC EQUATIONS [J].
Castro, Angel ;
Cordoba, Diego ;
Gomez-Serrano, Javier .
DUKE MATHEMATICAL JOURNAL, 2016, 165 (05) :935-984
[6]   AN ANALYTICAL AND NUMERICAL STUDY OF STEADY PATCHES IN THE DISC [J].
De La Hoz, Francisco ;
Hassainia, Zineb ;
Hmidi, Taoufik ;
Mateu, Joan .
ANALYSIS & PDE, 2016, 9 (07) :1609-1670
[7]   DOUBLY CONNECTED V-STATES FOR THE PLANAR EULER EQUATIONS [J].
De la Hoz, Francisco ;
Hmidi, Taoufik ;
Mateu, Joan ;
Verdera, Joan .
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2016, 48 (03) :1892-1928
[8]   Doubly Connected V-States for the Generalized Surface Quasi-Geostrophic Equations [J].
de la Hoz, Francisco ;
Hassainia, Zineb ;
Hmidi, Taoufik .
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2016, 220 (03) :1209-1281
[9]   VORTEX WAVES - STATIONARY V STATES, INTERACTIONS, RECURRENCE, AND BREAKING [J].
DEEM, GS ;
ZABUSKY, NJ .
PHYSICAL REVIEW LETTERS, 1978, 40 (13) :859-862
[10]   Imperfect Bifurcation for the Quasi-Geostrophic Shallow-Water Equations [J].
Dritschel, David Gerard ;
Hmidi, Taoufik ;
Renault, Coralie .
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2019, 231 (03) :1853-1915
1234