Orbital stability of periodic waves for the Klein-Gordon-Schrödinger system
Macroscopic discrete modelling of stochastic reaction-diffusion equations on a periodic domain
March 2011, 31(1): 239-252. doi: 10.3934/dcds.2011.31.239
Attractors for the three-dimensional incompressible Navier-Stokes equations with damping
Xue-Li Song 1, and Yan-Ren Hou 1,
College of science, Xi'an Jiaotong University, Xi'an, 710049, China, China
Received March 2010 Revised October 2010 Published June 2011
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..
Mathematics Subject Classification: Primary: 35B40, 35Q30; Secondary: 37L3.
Citation: Xue-Li Song, Yan-Ren Hou. Attractors for the three-dimensional incompressible Navier-Stokes equations with damping. Discrete & Continuous Dynamical Systems - A, 2011, 31 (1) : 239-252. doi: 10.3934/dcds.2011.31.239
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Xue-Li Song Yan-Ren Hou