Averaging of a multi-layer quasi-geostrophic equations with oscillating external forces
Article
Tachim Medjo, T. (2014). Averaging of a multi-layer quasi-geostrophic equations with oscillating external forces
. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 13(3), 1119-1140. 10.3934/cpaa.2014.13.1119
Tachim Medjo, T. (2014). Averaging of a multi-layer quasi-geostrophic equations with oscillating external forces
. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 13(3), 1119-1140. 10.3934/cpaa.2014.13.1119
In this article, we consider a non-autonomous multi-layer quasigeostrophic equations of the ocean with a singularly oscillating external force g ∈= go(t) + ∈-p g1(t/∈) depending on a small parameter ∈ > 0 and ρ ∈ [0, 1) together with the averaged system with the external force g0(t), formally corresponding to the case ∈ = 0. Under suitable assumptions on the external force, we prove as in [10] the boundness of the uniform global attractor A ∈ as well as the upper semi-continuity of the attractors A ∈ of the singular systems to the attractor A0 of the averaged system as ∈ → 0+. When the external force is small enough and the viscosity is large enough, the convergence rate is controlled by K∈(1-ρ). 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].
