McKean-Vlasov Stochastic Partial Differential Equations: Existence, Uniqueness and Propagation of Chaos

2023/06/27 by Wei Hong, Hong, Wei, Shihu Li +3 · 1 citation
Economics, Econometrics and Finance · Engineering · Mathematics · #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Mathematical Biology Tumor Growth #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2306.15508

openalex publication_date 2023/06/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we provide a general framework for investigating McKean-Vlasov stochastic partial differential equations. We first show the existence of weak solutions by combining the localizing approximation, Faedo-Galerkin technique, compactness method and the Jakubowski version of the Skorokhod representation theorem. Then under certain locally monotone condition we further investigate the existence and uniqueness of (probabilistically) strong solutions. The applications of the main results include a large class of McKean-Vlasov stochastic partial differential equations such as stochastic 2D/3D Navier-Stokes equations, stochastic Cahn-Hilliard equations and stochastic Kuramoto-Sivashinsky equations. Finally, we show a propagation of chaos result in Wasserstein distance for weakly interacting stochastic 2D Navier-Stokes systems.

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• McKean-Vlasov SPDEs driven by Poisson random measure: Well-posedness and large deviation principle

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