Existence of the stationary Navier-Stokes flow in $\mathbb{R}^2$ around a radial flow

Abstract

We consider the stationary Navier-Stokes equations on the whole plane $\mathbb{R}^2$. We show that for a given small and smooth external force around a radial flow, there exists a classical solution decaying like $|x|^{-1}$. In our result, it is not necessary to impose any symmetric conditions on external forces.