Uniqueness for stochastic scalar conservation laws on Riemannian manifolds revisited

Abstract

We revise a uniqueness question for the scalar conservation law with stochastic forcing du + divgf(x,u)dt = ?(x,u)dWt, x ? M, t ? 0 on a smooth compact Riemannian manifold (M,g) whereWt is the Wiener process and x ? f(x,?) is a vector field on M for each ? ? R. We introduce admissibility conditions, derive the kinetic formulation and use it to prove uniqueness in a more straight-forward way than in the existing literature.