2022/06/10 by Qian, Zhongmin · 1 citation
#35Q30 #35Q35 #60H30 #76D03 #76D05 #76D17 #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Probability (math.PR)
paper · doi:10.48550/arxiv.2206.05198
In this paper we establish a mathematical framework which may be used to design Monte-Carlo simulations for a class of time irreversible dynamic systems, such as incompressible fluid flows, including turbulent flows in wall-bounded regions, and some other (non-linear) dynamic systems. Path integral representations for solutions of forward parabolic equations are obtained, and, in combining with the vorticity transport equations, probabilistic formulations for solutions of the Navier-Stokes equations are therefore derived in terms of (forward) McKean-Vlasov stochastic differential equations (SDEs), which provides us with the mathematical framework for Monte-Carlo simulations of wall-bounded turbulent flows.