Abstract:
We prove that if $u$ is a suitable weak solution to the three dimensional Navier–Stokes equations from the space $L_{\infty}(0,T;\dot{B}_{\infty,\infty}^{-1})$, then all scaled energy quantities of $u$ are bounded. As a consequence, it is shown that any axially symmetric suitable weak solution $u$, belonging to $L_{\infty}(0,T;\dot{B}_{\infty,\infty}^{-1})$, is smooth.
Key words and phrases:Navier–Stokes equations, suitable weak solutions, Besov spaces.