On the long-time stability of a temporal discretization scheme for the three dimensional viscous primitive equations

Abstract

In this article, a semi-discretized Euler scheme to solve the three dimensional viscous primitive equations is studied. Based on suitable assumptions on the initial data and forcing terms, the long-time stability of the proposed scheme is proven by showing that the norm (in space variables) of the solutions is bounded at each time step when the time step satisfies certain smallness condition.