The exponential behavior of 3D stochastic primitive equations driven by
fractional noise
Abstract
In this article, we study the exponential behavior of 3D stochastic
primitive equations driven by fractional noise. Since fractional
Brownian motion is essentially different from Brownian motion, the
standard method via classic stochastic analysis tools is not available.
Here, we develop a method which is close to the method from dynamic
system to show that the weak solutions to 3D stochastic primitive
equations driven by fractional noise converge exponentially to the
unique stationary solution of primitive equations. This method may be
applied to other stochastic hydrodynamic equations and other noises
including Brownian motion and Lévy noise.