On the number of singular points of weak solutions to the Navier‐Stokes equations

We consider a suitable weak solution to the three‐dimensional Navier‐Stokes equations in the space‐time cylinder Ω × ]0, T[. Let Σ be the set of singular points for this solution and Σ (t) ≡ {(x, t) ∈ Σ}. For a given open subset ω ⊆ Ω and for a given moment of time t ∈]0, T[, we obtain an upper bound for the number of points of the set Σ(t) ⋒ ω.