Weak vorticity formulation for incompressible 2D Euler in domains with boundary Helena Nussenzveig Lopes Federal University of Rio de Janeiro In this talk we derive and discuss a weak vorticity formulation for the incompressible 2D Euler equations in a bounded domain with, possibly, k holes. We examine the interaction of incompressible 2D flows with material boundaries. Our focus is the dynamic behavior of the circulation of velocity around boundary components and the possible exchange between flow vorticity and boundary circulation in flows with vortex sheet initial data.