On stochastic conservation laws and Malliavin calculus
Kenneth Hvistendahl Karlsen and Erlend Briseid Storrøsten
Abstract: For stochastic conservation laws driven by a semilinear noiseterm, 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  and Bauzet, Vallet, and Wittbold , and in our view simplifies some of the proofs.
 C. Bauzet, G. Vallet, and P. Wittbold. The Cauchy problem for conservation laws with a multiplicative stochastic perturbation. J. Hyperbolic Differ. Equ. 9 (4):661–709, 2012 [MR3021756].
 J. Feng and D. Nualart. Stochastic scalar conservation laws. J. Funct. Anal. 255 (2):313–373, 2008 [MR2419964].