Streamlines concentration and application to the incompressible Navier-Stokes equations

Abstract

For a smooth domain $D$ containing the origin, we consider a vector field $u\in C^1(D\setminus \{0\},{\mathbb{R}}^3)$ with $\divg u \equiv 0$ and exclude certain types of possible isolated singularities at the origin, based on the geometry of streamlines that go near that possible singular point.