On vorticity and expansion-rate of fluid flows, conditional law duality and their representations

2023/08/15 by Zhongmin Qian, Qian, Zhongmin, Zihao Shen +1
Computer Science · Earth and Planetary Sciences · #35Q30 #76M23 #76M25 #76M35 #76N99 #Analysis of PDEs (math.AP) #Aquatic and Environmental Studies #Computational Physics and Python Applications #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Geophysics and Gravity Measurements #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.2308.08019

openalex publication_date 2023/08/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

By using a formulation of motion equations for a viscous (compressible) fluid flow in terms of the vorticity and the rate of expansion as the main fluid dynamical variables, an approximation model is established for compressible flows with slowly varied (over the space) fluid density. The probabilistic tools and the main ingredient such as the duality of conditional laws and the forward type Feynman-Kac formula are established for elliptic operators of second order, in order to formulate the corresponding random vortex method for a class of viscous compressible fluid flows, based on their approximation motion equations.

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