On the asymptotic stability analysis and the existence of time-periodic solutions of the primitive equations

In this article, we prove an asymptotic stability criterion for the solutions of primitive equations defined on a three-dimensional finite cylindrical domain with time-dependent forcing terms. Under a suitable smallness assumption on the nontrivial forcing terms, we obtain the existence of the time periodic solution for the primitive equations. Moreover, this time-periodic solution is asymptotically stable in L² sense.