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On strong solutions of the multi-layer quasi-geostrophic equations of the ocean

✍ Scribed by T. Tachim Medjo

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
327 KB
Volume
68
Category
Article
ISSN
0362-546X

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✦ Synopsis

In this article, we study the multi-layer quasi-geostrophic equations of the ocean. The existence of strong solutions is proved. We also prove the existence of a maximal attractor in L 2 (Ω ) and we derive estimates of its Hausdorff and fractal dimensions in terms of the data. Our estimates rely on a new formulation that we introduce for the multi-layer quasi-geostrophic equation of the ocean, which replaces the nonhomogeneous boundary conditions (and the nonlocal constraint) on the stream-function by a simple homogeneous Dirichlet boundary condition. This work improves the results given in [C. Bernier, Existence of attractor for the quasi-geostrophic approximation of the Navier-Stokes equations and estimate of its dimension, Adv. Math. Sci. Appl. 4 (2) (1994) 465-489].

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