Quasilinear parabolic stochastic partial differential equations: Existence, uniqueness

We present a direct approach to existence and uniqueness of strong (in the probabilistic sense) and weak (in the PDE sense) solutions to quasilinear stochastic partial differential equations, which are neither monotone nor locally monotone. The proof of uniqueness is very elementary, based on a new method of applying Ito's formula for the L-1-norm. The proof of existence relies on a recent regularity result and is direct in the sense that it does not rely on the stochastic compactness method. Crown Copyright (C) 2017 Published by Elsevier B.V. All rights reserved.