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Journal of Applied Nonlinear Dynamics 14(2) (2025) 263--270 | DOI:10.5890/JAND.2025.06.003

Mohammad Rahman, Kening Wang, Mei-Qin Zhan

Department of Mathematics and Statistics, University of North Florida, Jacksonville, FL32224, USA

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Abstract

In this article, we study the Semigeostrophic Equations in meteorology. These equations were introduced by Hoskins and Bretherton [1]. After suitable changes of variables, one can obtain the following coupled \MP problem \begin{eqnarray} \frac{\partial q}{\partial t} + J(\psi, q)=0 \nonumber\\ \Delta \phi + det(\frac{\partial^2 \phi}{\partial x_i \partial x_j})+ 1 = q\nonumber\\ \psi_{xx} \phi_{yy} - 2 \psi_{xy} \phi_{xy} + \psi_{yy} \phi_{xx} + \Delta \psi -\Delta \phi = 0 \nonumber \end{eqnarray} We proved the existence and uniqueness of time-periodic solution to the system.

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