Time periodic doubly connected solutions for the 3D quasi-geostrophic model

2022/06/21 by C. García, T. Hmidi, García, C. +3
Mathematics · #35B32 #35P30 #35Q35 #35Q86 #76U05 #Advanced Differential Equations and Dynamical Systems #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2206.10197

openalex publication_date 2022/06/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we construct time periodic doubly connected solutions for the 3D quasi-geostrophic model in the patch setting. More specifically, we prove the existence of nontrivial m-fold doubly connected rotating patches bifurcating from a generic doubly connected revolution shape domain with higher symmetry m≥ m₀ and m₀ is large enough. The linearized matrix operator at the equilibrium state is with variable and singular coefficients and its spectral analysis is performed via the approach devised in [27] where a suitable symmetrization has been introduced. New difficulties emerge due to the interaction between the surfaces making the spectral problem richer and involved.

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