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 31 条

[1]

[Anonymous], 1945, Hydrodynamics

[2] THE KELVIN WAVES IN VORTEX DYNAMICS AND THEIR STABILITY [J].

BURBEA, J ;

LANDAU, M .

JOURNAL OF COMPUTATIONAL PHYSICS, 1982, 45 (01) :127-156

[3] MOTIONS OF VORTEX PATCHES [J].

BURBEA, J .

LETTERS IN MATHEMATICAL PHYSICS, 1982, 6 (01) :1-16

[4] Uniformly Rotating Analytic Global Patch Solutions for Active Scalars [J].

Castro A. ;

Córdoba D. ;

Gómez-Serrano J. .

Annals of PDE, 2 (1)

[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] A new family of uniform vortices related to vortex configurations before merging [J].

Cerretelli, C ;

Williamson, CHK .

JOURNAL OF FLUID MECHANICS, 2003, 493 :219-229

[7]

Chemin J. -Y., 1998, Perfect Incompressible Fluids

[8]

Crandall M. G., 1971, J. Funct. Anal., V8, P321

[9] 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

[10] VORTEX WAVES - STATIONARY V STATES, INTERACTIONS, RECURRENCE, AND BREAKING [J].

DEEM, GS ;

ZABUSKY, NJ .

PHYSICAL REVIEW LETTERS, 1978, 40 (13) :859-862

← 1 2 3 4 →