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

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


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