揭示相对论流体动力学中的非正则哈密顿结构

Keiichiro Takeda , Naoki Sato
{"title":"揭示相对论流体动力学中的非正则哈密顿结构","authors":"Keiichiro Takeda ,&nbsp;Naoki Sato","doi":"10.1016/j.fpp.2025.100092","DOIUrl":null,"url":null,"abstract":"<div><div>We present the noncanonical Hamiltonian structure of the relativistic Euler equations for a perfect fluid in Minkowski spacetime. By identifying the system’s noncanonical Poisson bracket and Hamiltonian, we show that relativistic fluid flows preserve helicity and enstrophy as conserved quantities in three-dimensional and two-dimensional cases, respectively. This holds when the fluid follows a relativistic <span><math><mi>γ</mi></math></span>-barotropic equation of state, which generalizes the classical barotropic condition. Furthermore, we demonstrate that these conserved quantities are Casimir invariants associated with the noncanonical Poisson structure. These findings open new avenues for applying Hamiltonian theory to the study of astrophysical fluids and relativistic plasmas.</div></div>","PeriodicalId":100558,"journal":{"name":"Fundamental Plasma Physics","volume":"14 ","pages":"Article 100092"},"PeriodicalIF":0.0000,"publicationDate":"2025-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Revealing noncanonical Hamiltonian structures in relativistic fluid dynamics\",\"authors\":\"Keiichiro Takeda ,&nbsp;Naoki Sato\",\"doi\":\"10.1016/j.fpp.2025.100092\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>We present the noncanonical Hamiltonian structure of the relativistic Euler equations for a perfect fluid in Minkowski spacetime. By identifying the system’s noncanonical Poisson bracket and Hamiltonian, we show that relativistic fluid flows preserve helicity and enstrophy as conserved quantities in three-dimensional and two-dimensional cases, respectively. This holds when the fluid follows a relativistic <span><math><mi>γ</mi></math></span>-barotropic equation of state, which generalizes the classical barotropic condition. Furthermore, we demonstrate that these conserved quantities are Casimir invariants associated with the noncanonical Poisson structure. These findings open new avenues for applying Hamiltonian theory to the study of astrophysical fluids and relativistic plasmas.</div></div>\",\"PeriodicalId\":100558,\"journal\":{\"name\":\"Fundamental Plasma Physics\",\"volume\":\"14 \",\"pages\":\"Article 100092\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2025-04-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Fundamental Plasma Physics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S2772828525000093\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Fundamental Plasma Physics","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2772828525000093","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0

摘要

我们给出了闵可夫斯基时空中完美流体的相对论欧拉方程的非正则哈密顿结构。通过识别系统的非正则泊松括号和哈密顿量,我们证明了相对论性流体流动分别在三维和二维情况下保持螺旋度和熵作为守恒量。当流体遵循相对论性γ-正压状态方程时,这一点成立,它推广了经典的正压条件。此外,我们证明了这些守恒量是与非正则泊松结构相关的卡西米尔不变量。这些发现为将哈密顿理论应用于天体物理流体和相对论等离子体的研究开辟了新的途径。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Revealing noncanonical Hamiltonian structures in relativistic fluid dynamics
We present the noncanonical Hamiltonian structure of the relativistic Euler equations for a perfect fluid in Minkowski spacetime. By identifying the system’s noncanonical Poisson bracket and Hamiltonian, we show that relativistic fluid flows preserve helicity and enstrophy as conserved quantities in three-dimensional and two-dimensional cases, respectively. This holds when the fluid follows a relativistic γ-barotropic equation of state, which generalizes the classical barotropic condition. Furthermore, we demonstrate that these conserved quantities are Casimir invariants associated with the noncanonical Poisson structure. These findings open new avenues for applying Hamiltonian theory to the study of astrophysical fluids and relativistic plasmas.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
自引率
0.00%
发文量
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信