Abstract
In this paper, we study the partial regularity of fractional Navier–Stokes equations in \({\mathbb{R}^3 \times (0, \infty)}\) with \({3/4 < s < 1}\) . We show that the suitable weak solution is regular away from a relatively closed singular set whose (5−4s)-dimentional Hausdorff measure is zero. The result is a generalization of the partial regularity for the classical Navier–Stokes system in Caffarelli et al. (Commun Pure Appl Math 35:771–831, 1982).
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Tang, L., Yu, Y. Partial Regularity of Suitable Weak Solutions to the Fractional Navier–Stokes Equations. Commun. Math. Phys. 334, 1455–1482 (2015). https://doi.org/10.1007/s00220-014-2149-z
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DOI: https://doi.org/10.1007/s00220-014-2149-z