Euler-Lagrangian approach to stochastic Euler equations in Sobolev Spaces

The purpose of this paper is to establish the equivalence between Lagrangian and classical formulations for the stochastic incompressible Euler equations, the proof is based in Ito-Wentzell-Kunita formula and stochastic analysis techniques. Moreover, we prove a local existence result for the Lagrangian formulation in suitable Sobolev Spaces.