Boundary vorticity of incompressible 2D flows

TL;DR

This paper explores the boundary vorticity in incompressible 2D flows within bounded domains, analyzing the implications of Neumann pressure boundary conditions and their equivalence to boundary vorticity.

Contribution

It provides a rigorous investigation into the rigidity of boundary vorticity conditions under Neumann pressure boundary constraints in 2D incompressible flows.

Findings

Homogeneous Neumann boundary conditions imply constant boundary vorticity.

The study establishes conditions under which boundary vorticity is rigidly determined.

Results contribute to understanding boundary behavior in 2D fluid dynamics.

Abstract

For a homogeneous incompressible 2D fluid confined within a bounded Lipschitz simply connected domain, homogeneous Neumann pressure boundary conditions are equivalent to a constant boundary vorticity. We investigate the rigidity of such conditions.