Riemann Problem for Random Advective Equation

In this article we present an explicit expression to the solution of the random Riemann problem for the 1D random linear transport equation. We show that the random solution is a similarity solution and thestatistical moments have very simple expressions. We show that the mean, the variance, and the 3rd central moment agree quite well with Monte Carlo simulations. We guess that our approach can be useful in designing numerical methods for random transport equation, as in the deterministic case.