On the Asymptotic Stability Analysis and the Existence of Time-Periodic Solutions of the Primitive Equations

Abstract

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 L-2 sense.