带有指数阻尼项的三维Navier-Stokes方程吸引子的存在性

Existence of Attractors for the Three-Dimensional Navier-Stokes Equations with Exponential Damping

摘要: 近些年，带有多项式阻尼项的Navier-Stokes方程被推导且得到研究，并且得出了很多重要结论。本文证明了带有指数阻尼项$\alpha \left(e^{\beta {\left|u\right|}^2}-1\right)u\left(\alpha >0,\beta >0\right)$ 的三维Navier-Stokes方程在有界区域上整体吸引子的存在性。

Abstract: In recent years, the Navier-Stokes equations with polynomial damping have been derived and studied, and many important conclusions have been drawn. In this paper, we show that the three-dimensional Navier-Stokes equations with exponential damping $\alpha \left(e^{\beta {\left|u\right|}^2}-1\right)u\left(\alpha >0,\beta >0\right)$ have global attractors in the bounded domain.