In this paper, we establish the existence and uniqueness of both mild(/variational) solutions and weak (in the sense of PDE) solutions of coupled system of 2D stochastic Chemotaxis-Navier-Stokes equations. The mild/variational solution is obtained through introducing a new method of cutting off the stochastic system and using a fixed point argument in a carefully constructed Banach space. To get the weak solution we first prove the existence of a martingale weak solution and then we show that the pathwise uniqueness holds for the martingale solution.

中文翻译：

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2D随机趋化-Navier-Stokes系统

在本文中，我们建立了二维随机Chemotaxis-Navier-Stokes方程耦合系统的温和（变分）解和弱（在PDE意义上）解的存在性和唯一性。通过引入一种切断随机系统的新方法并在精心构建的Banach空间中使用不动点参数，可以得到温和/变分解。为了获得弱解，我们首先证明了weak弱解的存在，然后证明了the解的路径唯一性成立。