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arXiv · 2206.10197

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

C. García·T. Hmidi·J. Mateu
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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 $m\geq m_0$ and $m_0$ 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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C. García, T. Hmidi, J. Mateu. 2022-06-21. Time periodic doubly connected solutions for the 3D quasi-geostrophic model. https://arxiv.org/abs/2206.10197

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