AVERAGING OF A MULTI-LAYER QUASI-GEOSTROPHIC EQUATIONS WITH OSCILLATING EXTERNAL FORCES

作者：Medjo T Tachim^*

来源：Communications on Pure and Applied Analysis, 2014, 13(3): 1119-1140.

DOI：10.3934/cpaa.2014.13.1119

• Averaging
• multi-layer quasi-geostrophic
• global attractor
• oscillating force

In this article, we consider a non-autonomous multi-layer quasi-geostrophic equations of the ocean with a singularly oscillating external force g(epsilon) = g(0)(t) + epsilon(-rho) g(1)(t/epsilon) depending on a small parameter epsilon > 0 and rho is an element of [0,1) together with the averaged system with the external force g(0)(t), formally corresponding to the case epsilon = 0. Under suitable assumptions on the external force, we prove as in [10] the boundness of the uniform global attractor A(epsilon) as well as the upper semi-continuity of the attractors A(epsilon) of the singular systems to the attractor A(0) of the averaged system as epsilon -> 0(+). When the external force is small enough and the viscosity is large enough, the convergence rate is controlled by K epsilon((1-rho)). Let us mention that the non-homogenous boundary conditions (and the non-local constraint) present in the multi-layer quasi-geostrophic model makes the estimates more complicated, [3]. These difficulties are overcome using the new formulation presented in [25].

• 出版日期2014-5