Stochastic formulation of incompressible fluid flows in wall bounded regions

Zhongmin Qian

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arXiv · 2206.05198

Stochastic formulation of incompressible fluid flows in wall bounded regions

Zhongmin Qian

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Abstract

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.

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Zhongmin Qian. 2022-06-10. Stochastic formulation of incompressible fluid flows in wall bounded regions. https://arxiv.org/abs/2206.05198

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