On Isolated Singularities for the Stationary Navier-Stokes System

The classical problem of removable singularities is considered for solutions to the stationary Navier-Stokes system in dimension n >= 3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n\ge 3$$\end{document} 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\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n=4$$\end{document} it is proved that there are not distributional solutions, smooth away from the singularity and such that u(x)=O(|x|-1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$u(x)=O(|x|<^>{-1})$$\end{document}.