Functional integral representations for solutions of the motion equations for wall-bounded incompressible viscous flows, expressed (implicitly) in terms of distributions of solutions to stochastic differential equations of McKean-Vlasov type, are established by using a perturbation technique. These representations are used to obtain exact random vortex dynamics for wall-bounded viscous flows. Numerical schemes therefore are proposed and the convergence of the numerical schemes for random vortex dynamics with an additional force term is established. Several numerical experiments are carried out for demonstrating the motion of a viscous flow within a thin layer next to the fluid boundary.

翻译：通过使用微扰技术，建立了有界壁不可压缩粘性流运动方程解的泛函积分表示，这些表示（隐式地）以McKean-Vlasov型随机微分方程解的分布形式给出。利用这些表示，得到了有界壁粘性流的精确随机涡动力学。据此提出了数值方案，并建立了含附加力项的随机涡动力学数值方案的收敛性。通过多个数值实验，展示了流体边界附近薄层内粘性流的运动。