A ``horizontal" hyper--diffusion $3-D$ thermocline planetary geostrophic model: well-posedness and long time behavior
NSF| Collaborative Research: Mathematical Studies of Certain Geophysical Models ,
NSF| Collaborative Research: Mathematical Studies of Certain Geophysical Models
Cao, Chongsheng; Titi, Edriss S.; Ziane, Mohammed;
A ``horizontal" hyper--diffusion $3-D$ thermocline planetary geostrophic model: well-posedness and long time behavior
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 literal boundary which are observed numerically in other models.
32 pages
- University of Southern California United States
- University of California, Irvine United States
Mathematics - Analysis of PDEs, FOS: Mathematics, Analysis of PDEs (math.AP)
Mathematics - Analysis of PDEs, FOS: Mathematics, Analysis of PDEs (math.AP)
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