The concept of kinetic solution and well-posedness for 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 explain the main ideas on a deterministic model problem and show how this approach can be adapted to stochastic setting. In the remaining time I will present several well-posedness results for the case of hyperbolic, semilinear degenerate parabolic and quasilinear degenerate parabolic stochastic conservation laws.

The talk is based on joint works with Arnaud Debussche and Julien Vovelle.