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

Wei Hong; Shihu Li; Wei Liu

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arXiv · 2306.15508

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

Wei Hong·Shihu Li·Wei Liu

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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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BibTeX RIS

Wei Hong, Shihu Li, Wei Liu. 2023-06-27. McKean-Vlasov Stochastic Partial Differential Equations: Existence, Uniqueness and Propagation of Chaos. https://arxiv.org/abs/2306.15508

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