On stochastic conservation laws and Malliavin calculus

Abstract

For stochastic conservation laws driven by a semilinear noise term, we propose a generalization of the Kružkov entropy condition by allowing the Kružkov constants to be Malliavin differentiable random variables. Existence and uniqueness results are provided. Our approach sheds some new light on the stochastic entropy conditions put forth by Feng and Nualart [17] and Bauzet, Vallet, and Wittbold [2], and in our view simplifies some of the proofs.