Abstract
The current paper is devoted to 3D stochastic Ginzburg–Landau equations with degenerate random forcing. We establish the stability of stochastic systems by investigating the relationship between invariant measures under the action of transition semigroups corresponding to different sets of parameters. Towards this aim a new form of bound on the difference between solutions along with the spectral gap plays a significant role.
Acknowledgements
This paper was motivated mainly during a stay at the Mathematics Research Centre of the University of Warwick. The authors would like to thank Xue-mei Li, Martin Hairer and David Elworthy for their warm hospitality and useful discussions.
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The authors declare no competing non-financial/financial interests.
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All is available.
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Notes on contributors
Dengdi Chen
Dengdi Chen contributed to carrying out additional analyses and finalizing this paper.
Yan Zheng
Yan Zheng contributed the central idea and wrote the initial draft of the paper.