The exponential behaviour and stabilizability of stochastic 2D hydrodynamical type systems

Abstract

We study the exponential behaviour and stabilizability of the following abstract nonlinear stochastic evolution equation

where is a multiplicative white noise in time with spatial correlation. Applications to concrete models in fluid mechanics are also given.

Keywords:

• Stochastic 2D hydrodynamical type systems
• stationary solution
• exponential stability
• stabilization
• application

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by Vietnam National Foundation for Science and Technology Development (NAFOSTED) [grant number 101.02-2015.10].