Remarques sur l'unicité pour le système de Navier–Stokes tridimensionnel

Abstract

We give a result of uniqueness for the three-dimensional Navier–Stokes system; the class of uniqueness that we consider is L 2 ( ( 0 , T ) , H ˙ 1 / 2 ) ∩ C ( [ 0 , T ) , M 1 / 2 ) where M 1 / 2 is the space of pointwise multipliers from H ˙ 1 / 2 to H ˙ − 1 / 2 . We also give a very simple proof to the uniqueness of solutions in C ( [ 0 , T ) , L 3 ) . To cite this article: F. Marchand, M. Paicu, C. R. Acad. Sci. Paris, Ser. I 344 (2007).