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

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.