Abstract:
We will introduce a class of nonlinear kinetic equations of Vlasov type arising in various models from statistical physics and fluid mechanics.
The main feature of this class is that the transport field behaves like the gradient of some velocity moments of the unknown. We will discuss sharp conditions for well-posedness in Sobolev spaces for this class. Joint work with D. Han-Kwan (Nantes) and K. Carrapatoso (Ecole Polytechnique)