  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.
