On Isolated Singularities for the Stationary Navier–Stokes System

Abstract The classical problem of removable singularities is considered for solutions to the stationary Navier–Stokes system in dimension $$n\ge 3$$ n ≥ 3 and an old theorem of Shapiro (TAMS 187:335–363, 1974) is recovered and extended to solutions in a half ball vanishing on the flat boundary. Moreover, for $$n=4$$ n = 4 it is proved that there are not distributional solutions, smooth away from the singularity and such that $$u(x)=O(|x|^{-1})$$ u ( x ) = O ( | x | - 1 ) .