Strong Time-Periodic Solutions to the 3D Primitive Equations subject to Arbitrary Large Forces

We show that the three-dimensional primitive equations admit a strong time-periodic solution of period $T>0$, provided the forcing term $f\in L^2(0,\mathcal T; L^2(\Omega))$ is a time-periodic function of the same period. No restriction on the magnitude of $f$ is assumed. As a corollary, if, in particular, $f$ is time-independent, the corresponding solution is steady-state.