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

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

2003-07-25

arxiv.org/abs/math/0307344v1

Mathematics

Analysis of PDEs

32 pages

Scientific paper

10.1088/0951-7715/17/5/011

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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