A kinetic approach to stochastic conservation laws

Many basic equations in physiscs can be written in the form of conservation law. However, as it is common in the field of PDEs and SPDEs, classical or strong solutions do not exist in general and, on the other hand, weak solutions are not unique. The notion of kinetic formulation and kinetic solution turns out to be a very convenient tool to overcome these difficulties.

In this talk, I will present a well-posedness result for degenerate parabolic stochastic conservation laws and, in the case of hyperbolic stochastic conservation laws, discuss the hydrodynamic limit of an approximation in the sense of Bhatnagar-Gross-Krook.