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

This article is cited in 2 scientific papers (total in 2 papers)

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

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

Bibliographic databases:

Document Type: Article
UDC: 530.1+532.5+536
Received: February 23, 2016

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

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\pages 237--247
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    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  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    2. M. O. Katanaev, “Chern–Simons action and disclinations”, Proc. Steklov Inst. Math., 301 (2018), 114–133  mathnet  crossref  crossref  isi  elib  elib
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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