On the well-posedness of SPDEs with singular drift in divergence form

Abstract

We prove existence and uniqueness of strong solutions for a class of second-order stochastic PDEs with multiplicative Wiener noise and drift of the form $\mathrm{div}\gamma (\nabla \cdot )$, where $\gamma$ is a maximal monotone graph in ${\mathbb{R}}^n\times {\mathbb{R}}^n$ obtained as the subdifferential of a convex function satisfying very mild assumptions on its behavior at infinity. The well-posedness result complements the corresponding one in our recent work arXiv:1612.08260 where, under the additional assumption that $\gamma$ is single-valued, a solution with better integrability and regularity properties is constructed. The proof given here, however, is self-contained.

11 pages

References in corpus (1)

• Well-posedness for a class of doubly nonlinear stochastic PDEs of divergence type

Cited by in corpus (1)

• The stochastic viscous Cahn-Hilliard equation: well-posedness, regularity and vanishing viscosity limit