Strong existence and uniqueness for a class of quasilinear stochastic evolution equations

TL;DR

This paper proves the existence of strong solutions and their uniqueness for a class of quasilinear stochastic evolution equations on bounded domains, combining recent weak existence results with Yamada--Watanabe theory and an $L^1$-contraction argument.

Contribution

It introduces a novel approach that combines weak existence results in an $L^p$-setting with Yamada--Watanabe theory to establish strong solutions and pathwise uniqueness.

Findings

Existence of probabilistically strong solutions for the equations.

Pathwise uniqueness established via an $L^1$-contraction argument.

Results apply to quasilinear stochastic evolution equations on bounded domains.

Abstract

We establish existence of probabilistically strong solutions and pathwise uniqueness for a class of quasilinear stochastic evolution equations on bounded domains. Our results combine recent weak existence results for quasilinear stochastic evolution equations in an $L^p$-setting (with $p > 2$) with Yamada--Watanabe theory. To establish pathwise uniqueness, we rely on an $L^1$-contraction argument.