On the existence of solutions to the planar exterior Navier Stokes system

TL;DR

This paper proves the existence of solutions to the stationary incompressible Navier-Stokes equations in the exterior of a disk with specific boundary conditions, expanding understanding of fluid flow around obstacles.

Contribution

It establishes the existence of solutions for a broad set of boundary conditions without symmetry assumptions, filling a gap in the mathematical theory of exterior flows.

Findings

Existence of solutions proven for non-zero boundary conditions

Solutions exist without symmetry assumptions

Applicable to exterior flow problems around disks

Abstract

We consider the stationary incompressible Navier Stokes equation in the exterior of a disk B with non-zero Dirichlet boundary conditions on the disk and zero boundary conditions at infinity. We prove the existence of solutions for an open set of boundary conditions without symmetry.