Existence of algebraic vortex spirals

In incompressible inviscid flow, vortex sheets are curves across which the tangential velocity is discontinuous, with zero vorticity away from the curve. They occur in many important applications, for example from the trailing edge of wings in accelerating aircraft. Most such flows have rollup of vortex sheets into algebraic spirals. Although exact solutions with logarithmic spirals have been known since Prandtl, all attempts at rigorous existence proofs of algebraic vortex spirals have been unsuccessful. We present a proof of existence in the case of large number of branches.