Partial regularity of Solutions of Navier-Stokes equations

Abstract: In this paper, we study the singular set of 3-dimensional Navier-Stokes equations. Under the condition$\frac{1}{R^{\frac{3s}{q}+2-s}}\int^{R^{2}}{0}(\int{B_{R}}|u|^{q}dx)^{\frac{s}{q}}ds <C,$ for $(q,s)\in{(2,5),(5,2)},$ we use the backward uniqueness of parabolic equations to show that the Hausdorff dimension of the singular set is less than 1.