Averaging of 2D Navier–Stokes equations with singularly oscillating forces
Averaging of 2D Navier–Stokes equations with singularly oscillating forces
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DOI：
10.1088/0951-7715/22/2/006
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发表时间：
2009-02
期刊：
影响因子：
1.7
通讯作者：
V. Chepyzhov;V. Pata;M. Vishik
中科院分区：
文献类型：
--
作者：
V. Chepyzhov;V. Pata;M. Vishik
当ρ ∈ [0，1）且ε > 0时，考虑了具有奇异振动外力的非自治二维Navier-Stokes方程，以及形式上对应于极限情形ε = 0的平均方程.在适当的外力假设下，证明了相应的一致全局吸引子的一致有界性，以及当ε → 0+时第一个系统的吸引子收敛于第二个系统的吸引子.当平均方程的Grashof数较小时，to的收敛速度由Kε1−ρ控制。
For ρ ∊ [0, 1) and ε > 0, the nonautonomous 2D Navier–Stokes equations with singularly oscillating external force are considered, together with the averaged equations formally corresponding to the limiting case ε = 0. Under suitable assumptions on the external force, the uniform boundedness of the related uniform global attractors is established, as well as the convergence of the attractors of the first system to the attractor of the second one as ε → 0+. When the Grashof number of the averaged equations is small, the convergence rate of to is controlled by Kε1−ρ.