Existence and Uniqueness for Stochastic 2D Euler Flows with Bounded Vorticity

The strong existence and the pathwise uniqueness of solutions with ({L^{infty}})-vorticity of the 2D stochastic Euler equations are proved. The noise is multiplicative and it involves the first derivatives. A Lagrangian approach is implemented, where a stochastic flow solving a nonlinear flow equation is constructed. The stability under regularizations is also proved.