电子等离子体的多维静电振荡特性
On the properties of multidimensional electrostatic oscillations of an electron plasma
摘要：
我们考虑经典的柯西问题的方程组描述的三维任意静电振荡的冷等离子体，并介绍了一个迭代过程，允许估计的爆破时间从下面。这个过程是建设性的一个成功地获得双边估计的额外的数量取决于解决方案。我们表明，这是可能的情况下，一个和两个维度，以及零涡度的解决方案。对于二维初始数据具有径向对称性的特殊情况，得到了第一周期振荡破坏和保持光滑性的精细充分条件。此外，我们给出了一个例子，估计爆破时间的数据的数值结果存在，并讨论了我们的估计的粗糙度。
英文摘要：
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.
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