• 主题
高级搜索  >
历史搜索 清空历史
首页> 外文期刊>Zeitschrift fur Angewandte Mathematik und Mechanik >Vlasov-Poisson Systems with Measures as Initial Data
【24h】

Vlasov-Poisson Systems with Measures as Initial Data

机译：量度为初始数据的Vlasov-Poisson系统

获取原文
获取原文并翻译 | 示例
           
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

This short exposition is about joint work done with Andrew Majda (Commu. Pure Appl. Math., 47(1994), 1365-1401), and Andrew Majda and George Majda (Physica D, 74(1994), 268-300; 79(1994), 41-76). We are motivated by the study on the vortex sheet initial value problem for the 2-D incompressible Euler equations. A. Majda proposed to study the Vlasov-Poisson systems with measures as initial data to help finding hints for the vortex sheets problem. We consider Cauchy problems for both the one- and two-component Vlasov-Poisson systems and the related Fokker-Planck-Poisson system with measures as initial data in one space dimension. The existence of global weak solutions for the one-component problems has been obtained by the author and A. Majda. For the two-component Vlasov-Poisson system, however, bona fide measure-valued solutions are found in the limit of weakly converging approximate solutions, which are obtained through a procedure typical in physics and numerical computations. Weak solutions of the one-component Vlasov-Poisson system can have very strong finite time singularities. We have an explicit example of an exact weak solution which develops a Dirac point charge concentration at finite time from an initial datum which concentrates on a straight segement (called "an electron sheet") in the position vs. velocity plane. Other explicit examples of exact solutions have been constructed to demonstrate that the Cauchy problems for the Vlasov-Poisson systems have in general multiple weak solutions. A highly efficient numerical algorithm, developed by G. Majda, enables us to show numerically and clearly that different regularizations of the problems select different weak solutions. In particular, solutions of the Fokker-Planck-Poisson system converge as the Fokker-Planck term vanishes to a weak solution which is different from the limit of solutions from smoothing the same initial datum. There seems therefore to be no selection principles.
机译：这个简短的说明是关于与Andrew Majda（Commu。Pure Appl.Math。，47（1994），1365-1401）以及Andrew Majda和George Majda（Physica D，74（1994），268-300; 79）进行的联合工作。 （1994），41-76）。我们受到对二维不可压缩Euler方程涡旋片初值问题研究的推动。 A. Majda建议研究Vlasov-Poisson系统，并以量度作为初始数据，以帮助找到有关涡旋片问题的提示。我们考虑一维和两维Vlasov-Poisson系统以及相关的Fokker-Planck-Poisson系统的柯西问题，并将度量作为一个空间维度的初始数据。作者和A. Majda已经获得了针对单组分问题的全局弱解的存在。但是，对于两成分的Vlasov-Poisson系统，在弱收敛的近似解的极限中找到了真实的量测值解，这是通过物理和数值计算中典型的过程获得的。单组分Vlasov-Poisson系统的弱解可能具有非常强的有限时间奇点。我们有一个精确的弱解的显式示例，该解在有限的时间从初始基准发展出狄拉克点电荷浓度，该初始基准集中在位置与速度平面上的直线段（称为“电子片”）上。精确解的其他显式示例已被构造为证明Vlasov-Poisson系统的柯西问题通常具有多个弱解。由G. Majda开发的一种高效的数值算法使我们能够从数字上清楚地表明问题的不同正则化选择了不同的弱解。特别是，随着Fokker-Planck项消失为弱解，该Fokker-Planck-Poisson系统的解收敛，该弱解不同于通过平滑相同的初始基准面而得出的解的极限。因此似乎没有选择原则。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号