Abstract
Depending on the geometry of the domain, one can define—at least—three different Stokes operators with Dirichlet boundary conditions. We describe how the resolvents of these Stokes operators converge with respect to a converging sequence of domains.
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Acknowledgements
This work was supported by the ANR Project INFAMIE (Grant No. ANR-15-CE40-001). The understanding of this subject has benefited from discussions with Tom ter Elst. The author thanks the anonymous referees whose remarks greatly improved this manuscript.
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Dedicated to Professor Jean-Yves Chemin on the Occasion of His 60th Birthday
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Monniaux, S. Behaviour of the Stokes operators under domain perturbation. Sci. China Math. 62, 1167–1174 (2019). https://doi.org/10.1007/s11425-019-9517-x
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DOI: https://doi.org/10.1007/s11425-019-9517-x