The fractal dimension of the singular set for solutions of the Navier-Stokes system

We consider suitable weak solutions of the Navier-Stokes system in a bounded space-time domain D. We prove that the parabolic fractal dimension of the singular set is less than or equal to 135/82. We also introduce the concept of the parabolic fractal measure F-P(alpha) and prove that the fractal measure F-P(135/82) of the singular set is zero. For the Leray-Hopf weak solutions, we prove F-1/2(Sigma(T)) = 0, where Sigma(T) denotes the set of singular times on [0, T] and F-1/2 stands for the 1/2-dimensional fractal measure.