In this paper we consider approximate solution sequences of the incompressible 2D Euler equations with vortex sheet initial data, that is, initial Rows with locally bounded kinetic energy such that the initial vorticity has bounded total mass. We show that, for every gamma > 0, there exists a concentration set (in the sense of DiPerna and Majda) for these approximate solution sequences with Hausdorff dimension at most 2+gamma, in the following fluid dynamics situations: Row in a bounded domain, periodic flow, and flow in the full plane but with non-negative vorticity.46116518
