阻尼Navier-Stokes系统的渐近吸引子

The Asymptotic Attractor of the Damped Navier-Stokes System

中文关键词:  渐近吸引子  渐近解序列  阻尼Navier-Stokes方程

英文关键词:asymptotic attractor  asymptotic solution sequence  damped navier-stokes equation

中文摘要:

      本文通过构造一个有限维解序列,研究了二维阻尼驱动Navier-Stokes方程的渐近吸引子,并证明了该解序列在长时间内无限逼近全局吸引子,最后给出了渐近吸引子的维数估计.

英文摘要:

      In this paper, the asymptotic attractor of the $2$-$D$ damped and driven Navier-Stokes equation is studied by constructing a finite-dimensional solution sequence, and it is proved that this solution sequence approximates the global attractor infinitely after a long time. The dimension estimate of the asymptotic attractor is obtained in the end.