SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 2452-2475, January 2021.
We show propagation of moments in velocity for the three-dimensional Vlasov--Poisson system with a uniform magnetic field $B=(0,0,\omega)$ by adapting the work of Lions and 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 us 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.

中文翻译：

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具有均匀磁场的Vlasov-Poisson系统：矩和规律的传播

SIAM数学分析杂志，第53卷，第2期，第2452-2475页，2021年1月。
我们显示了具有均匀磁场$ B =（0,0， \ omega）$，通过改编Lions和Perthame的作品。所加的磁场有时还会产生奇异点，这些奇异点是回旋加速器周期$ t = \ frac {2 \ pi k} {\ omega} $，$ k \ mathbb {N} $的倍数。此结果还使我们能够显示解决方案的规律性传播。对于唯一性，我们通过证明具有有限的宏观密度的解集是唯一性类来扩展Loeper的结果。