Abstract

In this paper, we first introduce the concept of suitable weak solutions for the inhomogeneous Navier-Stokes equations. In the case when the initial density is close to a positive constant, by combining local energy inequality, Sobolev embedding, pressure estimate and blow-up analysis, we establish interior regularity criterion of suitable weak solutions. Finally, we show that the 1-D Hausdorff measure of the set of possible singular points of suitable weak solutions vanishes by applying the interior regularity criterion.

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