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MiS Preprint
55/2000
On the number of singular points of weak solutions to the Navier-Stokes equations
Gregory A. Seregin
Abstract
We consider a suitable weak solution to the three-dimensional Navier-Stokes equations in the space-time cylinder $\Omega \times ]0,T[$. Let $\Sigma$ be the set of singular points for this solution and $\Sigma(t) \equiv \{ (x,t)\in \Sigma \}$. For a given open subset $\omega \subseteq \Omega$ and for a given moment of time $t \in ]0,T[$, we obtain an upper bound for the number of points of the set $\Sigma (t) \cap \omega$.