Attractors for the three-dimensional incompressible Navier-Stokes equationswith damping

Xue-Li Song; Yan-Ren Hou

doi:10.3934/dcds.2011.31.239

Article Contents

2011, Volume 31, Issue 1: 239-252. Doi: 10.3934/dcds.2011.31.239

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Attractors for the three-dimensional incompressible Navier-Stokes equations with damping

Xue-Li Song^1, and
Yan-Ren Hou^1,

1.
College of science, Xi’an Jiaotong University, Xi’an, 710049

Received: February 28, 2010

Revised: September 30, 2010

Published: December 2010

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Abstract

In this paper, we show that the strong solution of the three-dimensional Navier-Stokes equations with damping $\alpha|u|^{\beta-1}u\ (\alpha>0, \frac{7}{2}\leq \beta\leq 5)$ has global attractors in $V$ and $H^2(\Omega)$ when initial data $u_0\in V$, where $\Omega\subset \mathbb{R}^3$ is bounded.

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Mathematics Subject Classification: Primary: 35B40, 35Q30; Secondary: 37L30.

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