In this four-hour course we aim at introducing an important kinetic-fluid system of partial differential equations describing the behaviour of a large population of very light particles immersed in a surrounding incompressible viscous fluid. The resulting non-linear system, in the particular scales imposed by combustion models, leads to a coupling between a Vlasov equation for the light particles and a Navier-Stokes system for the fluid. We review first some of the origins of the model, existence and uniqueness, and secondly we consider the long-time behaviour of the system, which produces a concentration phenomenon in velocity leading to a singular profile.
First session: Wednesday 21 February, 10.00-12.00 (Huxley 341)
Second session: Wednesday 28 February, 10.00-12.00 (Huxley 658)