论文标题
理想不可压缩的液体和磁性水力学的拉格朗日和狄拉克约束
Lagrangian and Dirac constraints for the ideal incompressible fluid and magnetohydrodynamics
论文作者
论文摘要
拉格朗日在拉格朗日（Lagrangian）（变性）公式中使用其乘数方法在所谓的Lagrangian变量描述中对流体流的不可压缩性约束。另一种选择是通过使用非规范泊松托架对Dirac的约束方法的概括在Eulerian变量描述中的不可压缩性。在这里，它显示了如何使用Dirac的方法在Lagrangian变量描述中的规范泊松支架和Eulerian描述中的非规范泊松支架中强加不可压缩性约束，从而允许密度的对流。两种情况都赋予了保留差异性的差异和明确表达式的无限尺寸测量流的动力学，并根据约束和原始变量给出了这种动力学的显式表达式。由于拉格朗日和欧拉保护法是不完全相同的，因此可以比较各种方法。
The incompressibility constraint for fluid flow was imposed by Lagrange in the so-called Lagrangian variable description using his method of multipliers in the Lagrangian (variational) formulation. An alternative is the imposition of incompressibility in the Eulerian variable description by a generalization of Dirac's constraint method using noncanonical Poisson brackets. Here it is shown how to impose the incompressibility constraint using Dirac's method in terms of both the canonical Poisson brackets in the Lagrangian variable description and the noncanonical Poisson brackets in the Eulerian description, allowing for the advection of density. Both cases give dynamics of infinite-dimensional geodesic flow on the group of volume preserving diffeomorphisms and explicit expressions for this dynamics in terms of the constraints and original variables is given. Because Lagrangian and Eulerian conservation laws are not identical, comparison of the various methods is made.
