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On partial regularity of suitable weak solutions to the stationary fractional Navier–Stokes equations in dimension four and five

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Abstract

In this paper, we investigate the partial regularity of suitable weak solutions to the multi-dimensional stationary Navier–Stokes equations with fractional power of the Laplacian (−Δ)α (n/6 ≤ α < 1 and α ≠ 1/2). It is shown that the n + 2 − 6α (3 ≤ n ≤ 5) dimensional Hausdorff measure of the set of the possible singular points of suitable weak solutions to the system is zero, which extends a recent result of Tang and Yu [19] to four and five dimension. Moreover, the pressure in ε-regularity criteria is an improvement of corresponding results in [1, 13, 18, 20].

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We thank the referees for their time and comments.

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Authors and Affiliations

  1. Department of Mathematics and Information Science, Zhengzhou University of Light Industry, Zhengzhou, 450002, P. R. China

    Xiao Li Guo

  2. Institute of Applied Physics and Computational Mathematics, Beijing, 100088, P. R. China

    Yue Yang Men

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  1. Xiao Li Guo
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Correspondence to Xiao Li Guo.

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Guo, X.L., Men, Y.Y. On partial regularity of suitable weak solutions to the stationary fractional Navier–Stokes equations in dimension four and five. Acta. Math. Sin.-English Ser. 33, 1632–1646 (2017). https://doi.org/10.1007/s10114-017-7125-z

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  • DOI: https://doi.org/10.1007/s10114-017-7125-z

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