A one-dimensional kinetic model of plasma dynamics with a transport field
A one-dimensional kinetic model of plasma dynamics with a transport field
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具有输运场的等离子体动力学的一维动力学模型
DOI：
10.3934/eect.2014.3.681
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发表时间：
2013
影响因子：
1.5
通讯作者：
S. Pankavich
中科院分区：
文献类型：
--
作者：
Charles Nguyen;J. Anderson;S. Pankavich
在无碰撞等离子体的基本模型Vlasov-Maxwell （VM）系统的激励下，我们考虑了一个相关的非线性系统，一个空间和一个动量维的偏微分方程。由于对（VM）方程的非相对论版本解的正则性知之甚少，我们研究了一个简化系统，该系统也缺乏相对论速度修正，并证明了柯西问题经典解的局域存在性和唯一性。对于初始数据的特殊选择，还证明了这些解的全局实时存在性。最后，我们提供了一个估计，它独立于初始数据的选择，产生相关字段的额外全局实时规律性。
Motivated by the fundamental model of a collisionless plasma, the Vlasov-Maxwell (VM) system, we consider a related, nonlinear system of partial differential equations in one space and one momentum dimension. As little is known regarding the regularity properties of solutions to the non-relativistic version of the (VM) equations, we study a simplified system which also lacks relativistic velocity corrections and prove local-in-time existence and uniqueness of classical solutions to the Cauchy problem. For special choices of initial data, global-in-time existence of these solutions is also shown. Finally, we provide an estimate which, independent of the choice of initial data, yields additional global-in-time regularity of the associated field.