On the exponential behaviour of stochastic evolution equations for non-Newtonian fluids

Abstract

We investigate the exponential long-time behaviour of the stochastic evolution equations describing the motion of a non-Newtonian fluids excited by multiplicative noise. Some results on the exponential convergence in mean square and with probability one of the weak probabilistic solution to the stationary solutions are given. We also prove an interesting result related to the stabilization of these stochastic evolution equations.

Keywords:

• stochastic evolution equations
• weak solution
• asymptotic behaviour
• non-Newtonian fluids
• bipolar fluids
• stabilization

AMS Subject Classifications:

• 60H15
• 35Q35
• 60H30
• 35R15

Acknowledgements

The research of the authors was supported by the University of Pretoria and the National Research Foundation South Africa. P.A. Razafimandimby is also very grateful to the support he received from The Abdus Salam International Center for Theoretical Physics, Italy.