Hausdorff dimension of random attractor for stochastic Navier-Stokes-Voight equations and primitive equations (Q536110)

The authors work with random attractors that are related to the asymptotic behaviour of random dynamical systems. They study a three dimensional stochastic Navier-Stokes-Voight model of viscoelastic incompressible fluid and three dimensional stochastic primitive equations with additive noise. In their previous works the authors showed that the long time dynamics of the above mentioned systems are captured by random attractors. By using the methods in [\textit{H. Crauel} and \textit{F. Flandoli}, J. Dyn. Differ. Equations 10, No.~3, 449--474 (1998; Zbl 0927.37031)], they proved that the Hausdorff dimension of the attractor is an invariant random variable, and it is bounded by \(d\), provided the random dynamics system contracts \(d\)-dimensional volumes exponentially fast.