On the Stochastic Regularization of 3D Euler Equations Through Random Diffusion

In this paper, we consider 3D stochastic incompressible Euler equations perturbed by a multiplicative noise term acting as a random diffusion. By introducing a random field to the diffusion coefficient and applying the Itô integral, we show that this noise induces a mathematical structure analogous to the Navier-Stokes equations. We establish local well-posedness through a contraction argument and a priori estimates for these stochastic parabolic equations. In addition, we show the global well-posedness results for small initial data belonging to Gevrey-type Fourier-Bessel potential spaces with high probability.