Article ID Journal Published Year Pages File Type
4610639 Journal of Differential Equations 2014 26 Pages PDF
Abstract

The partial regularity of the suitable weak solutions to the Navier–Stokes equations in RnRn with n=2,3,4n=2,3,4 and the stationary Navier–Stokes equations in RnRn for n=2,3,4,5,6n=2,3,4,5,6 are investigated in this paper. Using some elementary observation of these equations together with De Giorgi iteration method, we present a unified proof on the results of Caffarelli, Kohn and Nirenberg [1], Struwe [17], Dong and Du [5], and Dong and Strain [7]. Particularly, we obtain the partial regularity of the suitable weak solutions to the 4d non-stationary Navier–Stokes equations, which improves the previous result of [5], where Dong and Du studied the partial regularity of smooth solutions of the 4d Navier–Stokes equations at the first blow-up time.

Related Topics
Physical Sciences and Engineering Mathematics Analysis
Authors
, ,