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 $B=(0,0,\omega )$ by adapting the work of Lions, Perthame. The added magnetic field also produces singularities at times which are the multiples of the cyclotron period $t=\frac{2\pi k}{\omega },k\in \mathbb{N}$ . 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.

23 pages. All comments are welcome!