Existence of Vortex Patch Equilibria for Active Scalars Equations

作     者：Cuba, Edison 

作者机构：Mathematical and Computer Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia Department of Mathematics State University of Campinas Rua Sérgio Buarque de Holanda 651 Cidade Universitária Campinas São Paulo13083-859 Brazil 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2024年

核心收录：

主　　题：Vortex flow 

摘      要：In this paper, we investigate the existence of a finite number of vortex patches for the generalized surface quasi-geostrophic (gSQG) equations with α ∈ [1,2), focusing on configurations that may rotate uniformly, translate, or remain stationary. Using a desingularization technique, we reformulate the problem to resolve singularities arising in the point vortex limit. Assuming a nondegenerate equilibrium of the point vortices, we apply the implicit function theorem to construct time-periodic solutions to the gSQG equations, offering asymptotic descriptions of the vortex patch *** Codes 35Q35, 76B03, 76B47 Copyright © 2024, The Authors. All rights reserved.