Dynamics of stochastic three dimensional Navier-Stokes-Voigt equations on unbounded domains

作者：Tang Quoc Bao^*

来源：Journal of Mathematical Analysis and Applications, 2014, 419(1): 583-605.

DOI：10.1016/j.jmaa.2014.05.003

• Random dynamical systems
• Random attractors
• Stochastic Navier-Stokes-Voigt equations
• Energy equation method

The aim of this paper is to study the long time behavior of the following stochastic 3D Navier-Stokes-Voigt equation %26lt;br%26gt;u(t) - v Delta u - alpha(2)Delta u(t) + (u . del)u + del p = g(x) + epsilon hd omega/dt %26lt;br%26gt;in an arbitrary (bounded or unbounded) domain satisfying the Poincare inequality. By famous J. Ball%26apos;s energy equation method, we obtain a unique random attractor A(epsilon) for the random dynamical system generated by the equation. Moreover, we prove that the random attractor A(epsilon) tends to the global attractor A(0) of the deterministic equation in the sense of Hausdorff semi-distance as epsilon -%26gt; 0.

• 出版日期2014-11-1