Dissipative Euler Flows for Vortex Sheet Initial Data without Distinguished Sign

We construct infinitely many admissible weak solutions to the 2D incompressible Euler equations for vortex sheet initial data. Our datum has vorticity concentrated on a simple closed curve in suitable Hölder space and may not have distinguished sign. are obtained by means of convex integration; they smooth outside “turbulence” zone which grows linearly time around sheet. As by-product, this approach shows how growth turbulence is controlled local energy inequality measures maximal dissipation rate terms strength. © 2021 The Authors. Communications Pure Applied Mathematics published Wiley Periodicals LLC.