On convergence of arbitrary D-solution of steady Navier--Stokes system in 2D exterior domains

TL;DR

This paper proves that solutions to the steady Navier-Stokes equations in 2D exterior domains with finite energy converge uniformly at infinity without requiring symmetry or smallness conditions.

Contribution

It establishes convergence of arbitrary finite-energy solutions in 2D exterior domains without additional assumptions.

Findings

Solutions with finite Dirichlet integral converge uniformly at infinity

No symmetry or smallness conditions are needed for convergence

Results apply to general solutions in 2D exterior domains

Abstract

We study solutions to stationary Navier Stokes system in two dimensional exterior domain. We prove that any such solution with finite Dirichlet integral converges at infinity uniformly. No additional condition (on symmetry or smallness) are assumed.