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A ``horizontal" hyper--diffusion $3-D$ thermocline planetary geostrophic model: well-posedness and long time behavior

Chongsheng Cao·Edriss S. Titi·Mohammed Ziane
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Abstract

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.

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Chongsheng Cao, Edriss S. Titi, Mohammed Ziane. 2003-07-25. A ``horizontal" hyper--diffusion $3-D$ thermocline planetary geostrophic model: well-posedness and long time behavior. https://doi.org/10.1088/0951-7715%2F17%2F5%2F011

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