Existence of planar non-symmetric stationary flows with large flux in an exterior disk

TL;DR

This paper proves the existence and uniqueness of non-symmetric stationary solutions to the 2D Navier-Stokes equations outside a disk with large flux, expanding understanding of fluid flows with critical decay.

Contribution

It demonstrates the existence of non-symmetric stationary flows with large flux around explicit solutions in an exterior disk, a novel result in fluid dynamics.

Findings

Solutions exist with critical decay rate $O(|x|^{-1})$

Solutions are unique within a certain class

Applicable to non-symmetric external forces

Abstract

This paper is concerned with the two-dimensional stationary Navier-Stokes system in the domain exterior to the unit disk. The existence of solutions with critical decay $O(|x|^{-1})$ is established around some explicit flows with large flux. The solutions are obtained for non-symmetric external forces, and moreover, are unique in a certain class.