5 papers
Stochastic PDEs with Generalized Coercivity: Global Well-Posedness and Finite Time Extinction
Wei Hong, Shihu Li, Wei Liu
This work investigates the global existence, uniqueness, and Feller property for stochastic partial differential equations under generalized coercivity conditions, particularly in…
Stochastic Forced 3D Navier-Stokes Equations in -Space
Wei Hong, Shihu Li, Wei Liu
In the classical work [FK], Fujita and Kato established the local existence of solutions to the 3D Navier-Stokes equations in the critical -space. In this paper,…
Mean Field Stochastic Partial Differential Equations with Nonlinear Kernels
Wei Hong, Shihu Li, Wei Liu
This work focuses on the mean field stochastic partial differential equations with nonlinear kernels. We first prove the existence and uniqueness of strong and weak solutions for m…
McKean-Vlasov Stochastic Partial Differential Equations: Existence, Uniqueness and Propagation of Chaos
Wei Hong, Shihu Li, Wei Liu
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…
McKean-Vlasov SPDEs driven by Poisson random measure: Well-posedness and large deviation principle
Yuhang Jiang, Jinming Li, Shihu Li
In this work, we investigate the McKean-Vlasov stochastic partial differential equations driven by Poisson random measure. By adapting the variational framework, we prove the well-…