Reflected stochastic partial differential equations with fully local monotone coefficients in infinite dimensional domains

Abstract

This paper establishes the well-posedness of stochastic partial differential equations with reflection in an infinite-dimensional ball, within the fully local monotone framework. Our result is very general, including many important models such as the stochastic Allen-Cahn equations, stochastic p-Laplacian equations and stochastic 3D tamed Navier-Stokes equations, as well as more complex systems like the stochastic Cahn-Hilliard equations and stochastic 2D liquid crystal models. The approach relies on the penalization method, pseudo-monotonicity techniques and Mazur's lemma.