Local and global existence of smooth solutions for the stochastic euler equations with multiplicative noise

We establish the local existence of pathwise solutions for the stochastic Euler equations in a three-dimensional bounded domain with slip boundary conditions and a suitable nonlinear multiplicative noise. In the twodimensional case we obtain the global existence of these solutions with additive or linear-multiplicative noise. Finally, we show that, in the threedimensional case, the addition of linear multiplicative noise provides a regularizing effect; the global existence of solutions occurs with high probability if the initial data is sufficiently small, or if the noise coefficient is sufficiently large.