摘要： 本文中，作者构造了一类耦合的有限维正倒向随机微分系统并考察其与不可压缩~Navier-Stokes~方程之间的联系，推广Feynman-Kac公式，为Navier-Stokes方程的解给出概率表示. 而且，利用概率分析的方法证明了这类正倒向随机微分系统局部解的存在唯一性，对于两维情形和小雷诺数情形，还进一步证明全局解的存在唯一性. Abstract: In this paper, we investigate a special coupled forward-backward stochastic differential system (FBSDS, for short) and generalize the well-known Feynman-Kac formula to obtain a probabilistic representation formula for the viscous incompressible Navier-Stokes equations. From an analytic point of view, a self-contained proof of the existence and uniqueness of the solution to this FBSDS which under regular conditions, also leads to a solution for the corresponding Navier-Stokes equation, is given with a probabilistic method and for two special small Reynolds number cases (with small initial values or large viscosity) and the two-dimensional case, the global results are respectively obtained as well.