Vortex patches choreography for active scalar equations
MetadataShow full item record
AuthorGarcía López, Claudia
Publisher version: García, C. Vortex Patches Choreography for Active Scalar Equations. J Nonlinear Sci 31, 75 (2021). [https://doi.org/10.1007/s00332-021-09729-x]
SponsorshipMINECO-Feder (Spain) RTI2018-098850-B-I00; Junta de Andalucia European Commission FQM 954 P18-RT-2422; MECD (Spain) FPU15/04094; European Research Council (ERC) European Commission ERC-StG-852741
This paper deals with the existence of N vortex patches located at the vertex of a regular polygon with N sides that rotate around the center of the polygon at a constant angular velocity. That is done for Euler and (SQG)β equations, with β∈(0,1), but may be also extended to more general models. The idea is the desingularization of the Thomsom polygon for the N point vortex system, that is, N point vortices located at the vertex of a regular polygon with N sides. The proof is based on the study of the contour dynamics equation combined with the application of the infinite dimensional Implicit Function theorem and the well--chosen of the function spaces.