A certain necessary condition of potential blow up for Navier-Stokes equations

We show that a necessary condition for $T$ to be a potential blow up time is $\lim\limits_{t\uparrow T}\|v(\cdot,t)\|_{L_3}=\infty$.Comment: 16 page

Unicité dans L 3 (R 3) et d'autres espaces fonctionnels limites pour Navier-Stokes

The main result of this paper is the proof of uniqueness for mild solutions of the Navier- Stokes equations in L 3 (R 3). This result is extended as well to some Morrey- Campanato spaces

Sur l'unicité dans L 3 (R 3 ) des solutions "mild'' des équations de Navier-Stokes. (French) [On the uniqueness in L 3 (R 3 ) of mild solutions for the Navier-Stokes equations]

We prove uniqueness in 1253-5 for mild solutions of the Navier-Stokes equations when the initial data are small enough. The proof lies on an estimate in the norm for the bilinear term.Nous prouvons l'unicit\ue9 dans L3(R3) des solutions mild des \ue9quations de Navier-Stokes lorsque la donn\ue9e initiale est de taille suffisamment petite. La d\ue9monstration repose sur l'estimation du terme bilin\ue9aire dans l'espace