On the steady Navier--Stokes equations in 2D exterior domains

TL;DR

This paper investigates the steady Navier--Stokes equations in 2D exterior domains, proving boundedness of solutions with finite Dirichlet integral and establishing existence under zero flux conditions.

Contribution

It provides new results on boundedness and existence of solutions for the 2D steady Navier--Stokes equations in exterior domains.

Findings

Solutions with finite Dirichlet integral are uniformly bounded.

Existence of solutions is proven under zero total flux assumption.

The study advances understanding of boundary value problems in fluid dynamics.

Abstract

We study the boundary value problem for the stationary Navier--Stokes system in two dimensional exterior domain. We prove that any solution of this problem with finite Dirichlet integral is uniformly bounded. Also we prove the existence theorem under zero total flux assumption.