An extension of an unicity class for Navier-Stokes equations

Abstract

This is a translation from French of my paper [R. May, Extension d'une classe d'unicite pour les equations de Navier-Stokes, Ann. I. H. Poincar\'{e}-AN 27 (2010) 705-718. doi:10.1016/j.anihp.2009.11.007]. Q. Chen, C. Miao, and Z. Zhang \cite{CMZ} have proved that weak Leray solutions of the Navier-Stokes are unique in the class $L^{\frac{2}{1+r}% }([0,T].B_{\infty}^{r,\infty}(\mathbb{R}^{3})$ with $r\in]-\frac{1}{2},1].$ In this paper, we establish that this criterion remains true for $r\in ]-1,-\frac{1}{2}].$