Lagrangian solutions to the Vlasov-Poisson system with a point charge
Lagrangian solutions to the Vlasov-Poisson system with a point charge
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点电荷 Vlasov-Poisson 系统的拉格朗日解
DOI：
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发表时间：
2017
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影响因子：
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通讯作者：
C. Saffirio
中科院分区：
文献类型：
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作者：
Gianluca Crippa;Silvia Ligabue;C. Saffirio
我们考虑三维空间中排斥性弗拉索夫-泊松系统的柯西问题，其中初始数据是漫射密度（假设有界且可积）与点电荷的总和。在接近点电荷的扩散密度的一些衰减假设下，在总能量的范围内，并假设初始总扩散电荷严格小于一，我们证明了全局拉格朗日解的存在。我们的结果扩展了[16]的欧拉理论，证明解是由流动轨迹传输的。证明基于[8]中在具有各向异性规律的向量场设置中发展的 ODE 理论，其中向量场梯度的某些分量是测度的奇异积分。
We consider the Cauchy problem for the repulsive Vlasov-Poisson system in the three dimensional space, where the initial datum is the sum of a diffuse density, assumed to be bounded and integrable, and a point charge. Under some decay assumptions for the diffuse density close to the point charge, under bounds on the total energy, and assuming that the initial total diffuse charge is strictly less than one, we prove existence of global Lagrangian solutions. Our result extends the Eulerian theory of [16], proving that solutions are transported by the flow trajectories. The proof is based on the ODE theory developed in [8] in the setting of vector fields with anisotropic regularity, where some components of the gradient of the vector field is a singular integral of a measure.