论文标题
关于电子等离子体的多维静电振荡的性能
On the properties of multidimensional electrostatic oscillations of an electron plasma
论文作者
论文摘要
我们考虑了描述冷等离子体的3D任意静电振荡的方程系统的经典库奇问题，并引入了迭代程序，该程序允许从下面估算爆破时间。如果一个人成功获得了额外数量的双面估计，则此过程是建设性的。我们表明，在一个和二维的情况下，以及涡度为零的解决方案是可能的。对于具有径向对称性的二维初始数据的特定情况，可以在振荡的第一阶段进行精制的足够条件，以破坏和保存平稳性。此外，我们给出了估计存在数字结果并讨论我们估计值的数据的爆炸时间的示例。
We consider the classical Cauchy problem for a system of equations describing 3D arbitrary electrostatic oscillations of the cold plasma and introduce an iteration procedure that allows estimating the blow-up time from below. This procedure is constructive provided one succeed to obtain a two-sided estimate of an additional quantity depending on the solution. We show that this is possible in the case of one and two dimensions, as well as for solutions with zero vorticity. For the particular case of two-dimensional initial data with the radial symmetry, refined sufficient conditions for destruction and preservation of smoothness in the first period of oscillations are obtained. Moreover, we give the example of estimating the blow-up time for the data for which results of numerics exist and discuss a roughness of our estimate.
