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The stochastic 2D primitive equations with anisotropic viscosity  are studied in this paper. The existence of the martingale solutions and pathwise uniqueness of the solutions are obtained. The proof is based on anisotropic estimates, the compactness method, tightness criteria and the Jakubowski version of the Skorokhod Theorem for nonmetric spaces.

Martingale Solutions of the Stochastic 2D Primitive Equations with Anisotropic Viscosity