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Asymptotic Log-Harnack Inequality and Ergodicity for 3D Leray-α Model with Degenerate Type Noise

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Abstract

The asymptotic log-Harnack inequality is proved for Leray-α model with degenerate type noise using the asymptotic coupling method. In particular, we don’t impose any lower bound assumption for the viscosity constant. As applications, we also derive ergodicity and further asymptotic properties for stochastic 3D Leray-α model.

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Acknowledgments

The authors want to express their gratitude to the editors and the referees for many helpful suggestions.

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Authors and Affiliations

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

    Wei Hong, Shihu Li & Wei Liu

  2. Center for Applied Mathematics, Tianjin University, Tianjin, 300072, China

    Wei Hong

  3. Research Institute of Mathematical Sciences, Jiangsu Normal University, Xuzhou, 221116, China

    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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Supported by NNSFC (No.11822106, 11831014) and the PAPD of Jiangsu Higher Education Institutions.

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Hong, W., Li, S. & Liu, W. Asymptotic Log-Harnack Inequality and Ergodicity for 3D Leray-α Model with Degenerate Type Noise. Potential Anal 55, 477–490 (2021). https://doi.org/10.1007/s11118-020-09865-1

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