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Asymptotic log-Harnack inequality and applications for stochastic 2D hydrodynamical-type systems with degenerate noise

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Abstract

In this paper, an asymptotic log-Harnack inequality and some consequent properties are established via the asymptotic coupling method for a class of stochastic 2D hydrodynamical-type systems driven by degenerate noise. The main results are applicable to the stochastic 2D Navier–Stokes equations, stochastic 2D magneto-hydrodynamic equations and stochastic 2D Boussinesq equations, stochastic 2D magnetic Bénard problem, stochastic 3D Leray-\(\alpha \) model and also stochastic shell models of turbulence in the degenerate noise case.

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Acknowledgements

The authors would like to thank the referees for their very valuable suggestions and constructive comments. This work is supported by NSFC (Nos. 11822106, 11831014, 11571147) and the PAPD of Jiangsu Higher Education Institutions.

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  1. School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, 221116, China

    Wei Hong, Shihu Li & Wei Liu

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  1. Wei Hong
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  2. Shihu Li
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  3. Wei Liu
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Correspondence to Wei Liu.

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Hong, W., Li, S. & Liu, W. Asymptotic log-Harnack inequality and applications for stochastic 2D hydrodynamical-type systems with degenerate noise. J. Evol. Equ. 21, 419–440 (2021). https://doi.org/10.1007/s00028-020-00587-w

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