Partial Regularity of Suitable Weak Solutions to the Fractional Navier–Stokes Equations

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).