A note on weak solutions to the Navier-Stokes equations that are locally in $L_\infty(L^{3,\infty})$

Abstract

The aim of the note is to proof a regularity result for weak solutions to the Navier-Stokes equations that are locally in $L_\infty(L^{3,\infty})$. It reads that, in a sense, the number of singular points at each time is at most finite. Our note is inspired by the paper of H. J. Choe, J. Wolf, M. Yang [1].