THE LIMIT alpha - 0 OF THE alpha-EULER EQUATIONS IN THE HALF-PLANE WITH NO-SLIP BOUNDARY CONDITIONS AND VORTEX SHEET INITIAL DATA

In this article we study the limit when alpha -> 0 of solutions to the alpha-Euler system in the half-plane, with no-slip boundary conditions. We establish the existence of subsequences converging to a weak solution of the 2D incompressible Euler equations, assuming nonnegative initial vorticities in the space of bounded Radon measures in H-1. This result extends the analysis done in [A. V. Busuioc and D. Iftimie, Nonlinearity, 30 (2017), pp. 4534-4557; M. C. Lopes Filho et al., Phys. D, 292-293 (2015), pp. 51-61]. It requires a substantially distinct approach, analogous to that used for Delort's theorem, and a new detailed investigation of the relation between (no-slip) filtered velocity and potential vorticity in the half-plane.