Dynamics of Partial Differential Equations
Volume 7 (2010)
Hausdorff dimension of random attractor for stochastic Navier-Stokes-Voight equations and primitive equations
Pages: 307 – 326
We study the three dimensional stochastic Navier-Stokes-Voight model of viscoelastic incompressible fluid and three dimensional stochastic Primitive Equations with additive noise. In  and , we showed that the long time dynamics is captured by a random attractor, along this line, in this paper, we show that the Hausdorff dimension of attractor is an invariant random variable, and it is bounded by d, provided the random dynamics system contracts d-dimensional volumes exponentially fast.
Hausdorff dimension, Navier-Stokes-Voight equations, primitive equations
2010 Mathematics Subject Classification
Primary 35Qxx, 60H15. Secondary 76M35, 86A05, 86A10.