Partial Hölder regularity of the steady fractional Navier–Stokes equations

Abstract

In this paper, we study steady suitable weak solutions to the fractional Navier–Stokes system in \(\mathbb {R}^3\) with \(1/2 < s < 1\), where s denotes the power of the negative Laplacian. We show that if \(1/2<s<5/6\), any steady suitable weak solution is regular away from a relatively closed set with zero \((5-6s)\)-Hausdorff measure and it is regular when \(5/6\le s<1\).