The Vlasov-Poisson system with a uniform magnetic field: propagation of moments and regularity
Abstract
We show propagation of moments in velocity for the 3-dimensional Vlasov-Poisson system with a uniform magnetic field B = (0, 0, ω) by adapting the work of Lions, Perthame. The added magnetic field also produces singularities at times which are the multiples of the cyclotron period t = 2π kω, k ∈ N . This result also allows to show propagation of regularity for the solution. For uniqueness, we extend Loeper's result by showing that the set of solutions with bounded macroscopic density is a uniqueness class.
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