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

TL;DR

This paper proves the existence of classical solutions to the stationary Navier-Stokes equations in two dimensions around a radial flow with small, smooth external forces, without symmetry restrictions.

Contribution

It establishes the existence of solutions decaying like |x|^{-1} for small, smooth external forces in , without symmetry assumptions.

Findings

Existence of solutions decaying as |x|^{-1}

Solutions hold for small, smooth external forces

No symmetry conditions required on external forces

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.