References & Citations
Mathematics > Analysis of PDEs
Title: Existence of stationary vortex patches for the gSQG in bounded domains
(Submitted on 13 May 2024)
Abstract: 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 $\gamma$ 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.
Submission history
From: Lucas C. F. Ferreira [view email][v1] Mon, 13 May 2024 02:00:19 GMT (27kb)
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