Transport equations with disparate advection fields. Application to the gyrokinetic models in plasma physics

The subject matter of this paper concerns the asymptotic regimes for transport equations with advection fields having components of very disparate orders of magnitude. The main purpose is to derive the limit models: we justify rigorously the convergence towards these limit models and we investigate the well-posedness of them. Such asymptotic analysis arises in the magnetic confinement context, where charged particles move under the action of strong magnetic fields. In these situations we distinguish between a slow motion driven by the electric field and a fast motion around the magnetic lines.