# The vorticity equations in a half plane with measures as initial data

## TL;DR

This paper investigates the well-posedness of 2D Navier-Stokes vorticity equations in a half-plane with initial data as finite measures, establishing local and global results based on measure properties.

## Contribution

It introduces new well-posedness results for vorticity equations with measure initial data, utilizing $L^{1}$-estimates of the solution operator.

## Key findings

- Local well-posedness for measures with small pure point part
- Global well-posedness for measures with small total variation
- Development of $L^{1}$-estimates for the associated solution operator

## Abstract

We consider the two-dimensional Navier-Stokes equations subject to the Dirichlet boundary condition in a half plane for initial vorticity with finite measures. We study local well-posedness of the associated vorticity equations for measures with a small pure point part and global well-posedness for measures with a small total variation. Our construction is based on an $L^{1}$-estimate of a solution operator for the vorticity equations associated with the Stokes equations.