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Gromov–Hausdorff stability of global attractors for the 3D Navier–Stokes equations with dam**

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Abstract

This paper is concerned with the Gromov–Hausdorff stability of global attractors for the 3D Navier–Stokes equations with dam** under variations of the domain, which describes the complexity of the dynamics of the motion of a fluid flow. The Gromov–Hausdorff stability accounts for the Gromov–Hausdorff distance between two global attractors which may lie in disjoint phase spaces, as well as the stability of global attractors under perturbations of the domain. The same phase space cannot be used for the convergence via the Gromov–Hausdorff distance, which can be overcome, following Lee et al.(2020), by introducing a Banach space defined on a variable domain without “pull-backing” the perturbed system onto the original domain.

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Acknowledgements

The authors wish to thank an anonymous referee for her/his careful reading of the paper and useful comments. This work was partially supported by the Cultivation Fund of Henan Normal University (No. 2020PL17), Henan Overseas Expertise Introduction Center for Discipline Innovation (No. CXJD2020003), and Key Project of Henan Education Department (No. 22A110011). The authors also acknowledge fruitful discussion with Dr. **aona Cui from Henan Normal University on this topic which leads to an improvement of the paper.

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Authors and Affiliations

  1. Department of Mathematics and Information Science, Henan Normal University, **nxiang, 453007, People’s Republic of China

    Zhengwang Tao, **n-Guang Yang & Alain Miranville

  2. Laboratoire de Mathématiques et Applications, SP2MI, Boulevard Marie et Pierre Curie-Téléport 2, 86962, Chasseneuil Futuroscope Cedex, France

    Alain Miranville

  3. School of Mathematics, Tian** University, Tian**, 300072, People’s Republic of China

    Desheng Li

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Correspondence to Alain Miranville.

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Tao, Z., Yang, XG., Miranville, A. et al. Gromov–Hausdorff stability of global attractors for the 3D Navier–Stokes equations with dam**. Z. Angew. Math. Phys. 75, 1 (2024). https://doi.org/10.1007/s00033-023-02146-y

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