Averaging of a 3D primitive equations with oscillating external forces

作者：Medjo T Tachim^*

来源：Applicable Analysis, 2013, 92(5): 869-900.

DOI：10.1080/00036811.2011.640628

• averaging
• 3D primitive equations
• global attractor
• oscillating force

In this article, we consider a non-autonomous three-dimensional primitive equations of the ocean with a singularly oscillating external force g epsilon=g 0(t)+epsilon g 1(t/epsilon) depending on a small parameter epsilon>0 and [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 [V.V. Chepyzhov, V. Pata, and M.M.I. Vishik, Averaging of 2D NavierStokes equations with singularly oscillating forces, Nonlinearity, 22 (2009), pp. 351370] the boundness of the uniform global attractor ?epsilon as well as the convergence of the attractors ?epsilon of the singular systems to the attractor ?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). Let us note that the main difference between this work and that of Chepyzhov et al. (2009) is that the non-linearity involved in the three-dimensional primitive equation is stronger than the one in the two-dimensional NavierStokes equations considered in Chepyzhov et al. (2009), which makes the analysis of the problem studied in this article more involved.

• 出版日期2013-5-1