论欧拉和拉格朗日描述中变分原理的对应关系

IF 1.7 3区 物理与天体物理 Q2 PHYSICS, MATHEMATICAL
A. V. Aksenov, K. P. Druzhkov
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引用次数: 0

摘要

考虑了连续介质力学方程在欧拉和拉格朗日描述下的变分原理之间的关系。结果表明,对于含欧拉变量的微分方程组,相应的拉格朗日描述与引入非局部变量有关。这些描述之间的联系是根据不同的覆盖而得到的。讨论了方程组的变分原理与其辛结构之间的关系。结果表明,如果拉格朗日变量下的方程组可以由变分原理导出,那么欧拉变量下的方程组就没有相应的变分原理。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On the Correspondence between the Variational Principles in the Eulerian and Lagrangian Descriptions

The relationship between the variational principles for equations of continuum mechanics in Eulerian and Lagrangian descriptions is considered. It is shown that, for a system of differential equations in Eulerian variables, the corresponding Lagrangian description is related to introducing nonlocal variables. The connection between the descriptions is obtained in terms of differential coverings. The relation between the variational principles of a system of equations and its symplectic structures is discussed. It is shown that, if a system of equations in Lagrangian variables can be derived from a variational principle, then there is no corresponding variational principle in the Eulerian variables.

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来源期刊
Russian Journal of Mathematical Physics
Russian Journal of Mathematical Physics 物理-物理:数学物理
CiteScore
3.10
自引率
14.30%
发文量
30
审稿时长
>12 weeks
期刊介绍: Russian Journal of Mathematical Physics is a peer-reviewed periodical that deals with the full range of topics subsumed by that discipline, which lies at the foundation of much of contemporary science. Thus, in addition to mathematical physics per se, the journal coverage includes, but is not limited to, functional analysis, linear and nonlinear partial differential equations, algebras, quantization, quantum field theory, modern differential and algebraic geometry and topology, representations of Lie groups, calculus of variations, asymptotic methods, random process theory, dynamical systems, and control theory.
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