A note on the existence of stationary vortex patches for the SQG equation in bounded domain

Cao, Daomin; Lai, Shanfa; Qin, Guolin

doi:10.1090/proc/16487

A note on the existence of stationary vortex patches for the SQG equation in bounded domain
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by Daomin Cao, Shanfa Lai and Guolin Qin

Proc. Amer. Math. Soc. 151 (2023), 4881-4891

DOI: https://doi.org/10.1090/proc/16487

Published electronically: June 30, 2023

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Abstract:

By studying the contour dynamics equation and using the implicit function theorem, we prove the existence of stationary vortex patches with fixed vorticity and total flux for each patch for the surface quasi-geostrophic equation in a bounded domain near non-degenerate critical points of the Kirchhoff-Routh function.

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