Time Periodic Doubly Connected Solutions for the 3D Quasi-Geostrophic Model García López, Claudia Hmidi, Taoufik Mateu, Joan 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. 2024-05-02T07:48:59Z 2024-05-02T07:48:59Z 2022-06-21 journal article Published version: Claudia García, Taoufik Hmidi, and Joan Mateu. Time Periodic Doubly Connected Solutions for the 3D Quasi-Geostrophic Model. SIAM Journal on Mathematical Analysis. 2023. 55:6, 6133-6193 [10.1137/22M1513666] https://hdl.handle.net/10481/91310 10.1137/22M1513666 eng info:eu-repo/grantAgreement/ERC/H2020/ERC-StG-852741 http://creativecommons.org/licenses/by-nc-nd/4.0/ open access Attribution-NonCommercial-NoDerivatives 4.0 Internacional Society for Industrial and Applied Mathematics