The purpose of this work is to prove the existence of a weak solution of the two-dimensional incompressible Euler equations on a noncylindrical domain consisting of a smooth, bounded, connected and simply connected domain undergoing a prescribed motion. We prove the existence of a weak solution for initial vorticity in L-p, for p > 1. This work complements a similar result by C. He and L. Hsiao, who proved existence assuming that the flow velocity is tangent to the moving boundary, see Ref. 6.171220352053