Weak solutions to the incompressible Euler equations with vortex sheet initial data

We construct infinitely many admissible weak solutions to the incompressible Euler equations with initial data given by the classical vortex sheet. The construction is based on the method introduced recently in De Lellis and Székelyhidi Jr. (2009, 2010) [2,3] using convex integration. In particular, the vorticity is not a bounded measure. Instead, the energy decreases in time due to a linearly expanding turbulent zone around the vortex sheet.