ncts

In this talk, three-dimensional viscous primitive equations are considered. Primitive equations are also called hydrostatic Navier-Stokes equations which are the governing equations of the motion of flows in geophysical fluid dynamics. The global in time strong solution for these models has been established by Cao and Titi and Kobelkov independently. In this talk, several time-stepping numerical schemes have been studied. We are interested in the study and discussion of the long-time stability of these numerical schemes, which is important for the study of the climate. In this talk, we will start with some examples which give that the long time behavior of numerical schemes could be problematic. Then, we will introduce the primitive equations, present the semi-discretized schemes and analyze and discuss these numerical schemes. This talk is based on the joint work with Chun-Hsuing Hsia.