Non-autonomous planetary 3D geostrophic equations with oscillating external force and its global attractor

In this article, we consider a non-autonomous three-dimensional planetary geostrophic model of the ocean with a singulary oscillating external force depending on a small parameter ϵϵ. We prove the existence of the uniform global attractor AϵAϵ. Furthermore, using the method of Chepyzhov and Vishik (2007) [3] in the case of the two-dimensional Navier–Stokes systems, we study the convergence of AϵAϵ as ϵϵ goes to zero.