Large Deviations Principle for Stochastic Scalar Conservation Laws
  We investigate large deviations for a family of conservative stochastic PDEs (conservation laws) in the asymptotic of jointly vanishing noise and viscosity. We obtain a first large deviations principle in a space of Young measures. The associated rate functional vanishes on a wide set, the so-called set of measure-valued solutions to the limiting conservation law. We therefore investigate a second order large deviations principle, thus providing a quantitative characterization of non-entropic solutions to the conservation law. 
Mauro Mariani