Two-scale expansion of a singularly perturbed convection equation (Q1606253)

A singularly perturbed Vlasov equation \(\partial_t f + v.\nabla_x f + ({\mathcal E}(x,t) + \varepsilon^{-1} v \times {\mathcal B}(x,t)).\nabla_v f = 0\) is investigated. Here \(0<\varepsilon\ll 1\) is a small parameter representing a large magnetic field. They derive asymptotic expansion with respect to \(\varepsilon\) and characterize the terms of expansion. The proofs of convergence make use of Allaire's two-scale convergence.