For incompressible fluids, the vorticity, or curl of the velocity vector field, is often used to study the fluid’s behavior. A key part of this analysis is the Biot-Savart Law, which allows one to express the velocity as a convolution of the vorticity and a singular kernel. Without sufficient decay of the vorticity at infinity, however, the convolution integral fails to converge and the Biot-Savart Law does not hold. In this talk, we will present an alternative to the Biot-Savart Law for the Euler equations known as the Serfati identity, which was first introduced by Ph. Serfati in 1995. We will then discuss how this identity can be used to analyze solutions to the Euler equations with vorticity lacking decay at infinity.