Vortex patches choreography for active scalar equations García López, Claudia This work has been partially supported by the MINECO-Feder (Spain) research Grant number RTI2018–098850-B–I00, the Junta de Andalucía (Spain) project FQM 954, the Junta de Andaluciía (Spain) research Grant P18–RT–2422 and the MECD (Spain) research Grant FPU15/04094 (C.G), European Research Council through Grant ERC-StG-852741 (CAPA). 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. 2022-01-20T11:45:33Z 2022-01-20T11:45:33Z 2020-10-14 journal article 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] http://hdl.handle.net/10481/72406 10.1007/s00332-021-09729-x eng info:eu-repo/grantAgreement/EC/H2020/ERC-StG-852741 http://creativecommons.org/licenses/by-nc-nd/3.0/es/ open access Atribución-NoComercial-SinDerivadas 3.0 España Springer Nature