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 -estimate of a solution operator for the vorticity equations associated with the Stokes equations.
Cite this article
Ken Abe, The vorticity equations in a half plane with measures as initial data. Ann. Inst. H. Poincaré Anal. Non Linéaire 38 (2021), no. 4, pp. 1055–1094DOI 10.1016/J.ANIHPC.2020.10.002