Pré-Publication, Document De Travail Année : 2021

The Vlasov-Poisson system with a uniform magnetic field: propagation of moments and regularity

Alexandre Rege
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Résumé

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 = 2πk ω , 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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Dates et versions

hal-02978956 , version 1 (26-10-2020)
hal-02978956 , version 2 (09-03-2021)

Identifiants

  • HAL Id : hal-02978956 , version 2

Citer

Alexandre Rege. The Vlasov-Poisson system with a uniform magnetic field: propagation of moments and regularity. 2021. ⟨hal-02978956v2⟩
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