Partial Regularity of Weak Solutions to the Navier—Stokes Equations in the Class $ L^{\infty}(0,T;\, L^3(\Omega)^3) $

Abstract.

We show that if v is a weak solution to the Navier—Stokes equations in the class $L^{\infty}(0,T;\, L^3(\Omega)^3)$ then the set of all possible singular points of v in $\Omega$, at every time $t_0\in(0,T)$, is at most finite and we also give the estimate of the number of the singular points.