2024/05/13 by Vladimir Angulo-Castillo, Angulo-Castillo, Vladimir, Edison Cuba +3
Computer Science · Mathematics · #35Q35 #76B03 #76B47 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.2405.07427
openalex publication_date 2024/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we show the existence of time-periodic vortex patches for the generalized surface quasi-geostrophic equation within a bounded domain. This construction is carried out for values of γ in the range of (1,2). The resulting vortex patches possess a fixed vorticity and total flux, and they are located in the neighborhood of critical points that are non-degenerate for the Kirchhoff--Routh equation. The proof is accomplished through a combination of analyzing the linearization of the contour dynamics equation and employing the implicit function theorem as well as carefully selected function spaces.