"Fractionally dissipative stochastic quasi-geostrophic type equations on $R^d$

A stochastic fractionally dissipative quasi-geostrophic type equation on ${\mathbb{R}}^{d}$ with a multiplicative Gaussian noise is considered. We prove the existence of a martingale solution. The construction of the solution is based on appropriate approximations, the compactness method, and the Jakubowski version of the Skorokhod Theorem for nonmetric spaces. In the 2D sub-critical case we also prove the pathwise uniqueness of the solutions.