Dynamics of Partial Differential Equations

Volume 7 (2010)

Number 4

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

Pages: 307 – 326

DOI: https://dx.doi.org/10.4310/DPDE.2010.v7.n4.a2

Authors

Hongjun Gao (Institute of Mathematics, School of Mathematical Science, Nanjing Normal University, Nanjing, China)

Chengfeng Sun (Institute of Mathematics, School of Mathematical Science, Nanjing Normal University, Nanjing, China)

Abstract

We study the three dimensional stochastic Navier-Stokes-Voight model of viscoelastic incompressible fluid and three dimensional stochastic Primitive Equations with additive noise. In [12] and [11], 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.

Keywords

Hausdorff dimension, Navier-Stokes-Voight equations, primitive equations

2010 Mathematics Subject Classification

Primary 35Qxx, 60H15. Secondary 76M35, 86A05, 86A10.

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Published 1 January 2010