RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
 General information Latest issue Forthcoming papers Archive Impact factor Guidelines for authors License agreement Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Trudy MIAN: Year: Volume: Issue: Page: Find

 Tr. Mat. Inst. Steklova, 2016, Volume 294, Pages 237–247 (Mi tm3743)

Fluid dynamics and thermodynamics as a unified field theory

V. P. Pavlova, V. M. Sergeevb

a Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia
b Center for Global Issues, Institute for International Studies, MGIMO University, pr. Vernadskogo 76, Moscow, 119454 Russia

Abstract: We study the problem of consistency of equations of continuum dynamics (using the Euler equations and the continuity equation as examples) and thermodynamic equations of state (for the specific free energy, entropy, and volume). We propose a variant of the Hamiltonian formulation of a model that combines the fluid dynamics of a potential flow of a compressible fluid or gas and local equilibrium thermodynamics into a unified field theory. Thermodynamic equations of state appear in this model as second-class constraint equations. As a consistency condition, there arises another second-class constraint requiring that the product of density and temperature should be independent of time. The model provides an in-principle possibility of finding the time dependence of the specific entropy of the arising dynamical system.

 Funding Agency Grant Number Russian Science Foundation 14-50-00005 The work of V. P. Pavlov (Sections 2, 4, and 5) is supported by the Russian Science Foundation under grant 14-50-00005 and performed in Steklov Mathematical Institute of Russian Academy of Sciences. Sections 1, 3, and 6 are written by V. M. Sergeev.

DOI: https://doi.org/10.1134/S0371968516030146

Full text: PDF file (164 kB)
First page: PDF file
References: PDF file   HTML file

English version:
Proceedings of the Steklov Institute of Mathematics, 2016, 294, 222–232

Bibliographic databases:

Document Type: Article
UDC: 530.1+532.5+536

Citation: V. P. Pavlov, V. M. Sergeev, “Fluid dynamics and thermodynamics as a unified field theory”, Modern problems of mathematics, mechanics, and mathematical physics. II, Collected papers, Tr. Mat. Inst. Steklova, 294, MAIK Nauka/Interperiodica, Moscow, 2016, 237–247; Proc. Steklov Inst. Math., 294 (2016), 222–232

Citation in format AMSBIB
\Bibitem{PavSer16} \by V.~P.~Pavlov, V.~M.~Sergeev \paper Fluid dynamics and thermodynamics as a~unified field theory \inbook Modern problems of mathematics, mechanics, and mathematical physics.~II \bookinfo Collected papers \serial Tr. Mat. Inst. Steklova \yr 2016 \vol 294 \pages 237--247 \publ MAIK Nauka/Interperiodica \publaddr Moscow \mathnet{http://mi.mathnet.ru/tm3743} \crossref{https://doi.org/10.1134/S0371968516030146} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3628503} \elib{http://elibrary.ru/item.asp?id=26601061} \transl \jour Proc. Steklov Inst. Math. \yr 2016 \vol 294 \pages 222--232 \crossref{https://doi.org/10.1134/S0081543816060146} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000386554900014} \elib{http://elibrary.ru/item.asp?id=27575377} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84992084047} 

• http://mi.mathnet.ru/eng/tm3743
• https://doi.org/10.1134/S0371968516030146
• http://mi.mathnet.ru/eng/tm/v294/p237

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. V. V. Zharinov, “Hamiltonian operators in differential algebras”, Theoret. and Math. Phys., 193:3 (2017), 1725–1736
2. M. O. Katanaev, “Chern–Simons action and disclinations”, Proc. Steklov Inst. Math., 301 (2018), 114–133
•  Number of views: This page: 175 References: 23 First page: 8