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We study in this article the stochastic Zakharov-Kuznetsov equation driven bya multiplicative noise. We establish, in space dimensions two and three theglobal existence of martingale solutions, and in space dimension two the globalpathwise uniqueness and the existence of pathwise solutions. New methods areemployed in the passage to the limit on a special type of boundary conditionsand in the verification of the pathwise uniqueness of martingale solutions witha lack of regularity, where both difficulties arise due to the partlyhyperbolic feature of the model.

Martingale and Pathwise Solutions to the Stochastic Zakharov-Kuznetsov Equation with Multiplicative Noise