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

TL;DR

This paper proves the well-posedness of reflected stochastic PDEs with local monotone coefficients in infinite-dimensional domains, covering many significant models like stochastic Allen-Cahn and Navier-Stokes equations.

Contribution

It introduces a general framework for reflected stochastic PDEs with local monotone coefficients, including complex models such as stochastic Cahn-Hilliard and liquid crystal systems.

Findings

Established well-posedness for a broad class of reflected stochastic PDEs.

Included models like stochastic Allen-Cahn, p-Laplacian, and 3D tamed Navier-Stokes.

Extended to complex systems like stochastic Cahn-Hilliard and liquid crystal equations.

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.