A horizontal hyper-diffusion three-dimensional thermocline planetary geostrophic model: well-posedness and long-time behaviour

Chongsheng Cao, Edriss S Titi, Mohammed Ziane
2004 Nonlinearity  
In this paper we study a three dimensional thermocline planetary geostrophic "horizontal" hyper--diffusion model of the gyre-scale midlatitude ocean. We show the global existence and uniqueness of the weak and strong solutions to this model. Moreover, we establish the existence of a finite dimensional global attractor to this dissipative evolution system. Preliminary computational tests indicate that our hyper--diffusion model does not exhibit any of the nonphysical instabilities near the
more » ... ties near the literal boundary which are observed numerically in other models.
doi:10.1088/0951-7715/17/5/011 fatcat:eyvjo64ds5go3hevpys2owdqga