DCDS
Attractors for the three-dimensional incompressible Navier-Stokes equations with damping
Xue-Li Song Yan-Ren Hou
Discrete & Continuous Dynamical Systems - A 2011, 31(1): 239-252 doi: 10.3934/dcds.2011.31.239
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.
keywords: Global attractor Damping Weak solution Navier-Stokes equation Strong solution.
DCDS
Pullback $\mathcal{D}$-attractors for the non-autonomous Newton-Boussinesq equation in two-dimensional bounded domain
Xue-Li Song Yan-Ren Hou
Discrete & Continuous Dynamical Systems - A 2012, 32(3): 991-1009 doi: 10.3934/dcds.2012.32.991
We investigate the asymptotic behavior of solutions of a class of non-autonomous Newton-Boussinesq equation in two-dimensional bounded domain. The existence of pullback global attractors is proved in $L^2(\Omega)\times L^2(\Omega)$ and $H^1(\Omega)\times H^1(\Omega)$, respectively.
keywords: Pullback attractor Asymptotic compactness Newton-Boussinesq equation.

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