Stochastic 2D rotating Euler flows with bounded vorticity or white noise initial conditions

In this paper, we consider the stochastic two-dimensional (2D) rotating Euler equations with L-infinity initial conditions and white noise initial conditions, respectively. The existence and uniqueness of the equations with L-infinity vorticity are proved. The stability of beta tending to 0 for L-infinity initial conditions will be proved. At last, the case of white noise initial conditions is considered.