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Differential Invariants for Flows of Fluids and Gases

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Differential Geometry, Differential Equations, and Mathematical Physics

Abstract

The paper is an extended overview of the papers. The main extension is a detailed analysis of thermodynamic states, symmetries, and differential invariants. This analysis is based on consideration of Riemannian structure naturally associated with Lagrangian manifolds that represent thermodynamic states. This approach radically changes the description of the thermodynamic part of the symmetry algebra as well as the field of differential invariants.

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Acknowledgements

The authors wish to express their gratitude to referees for their helpful comments and remarks on the paper.

The research was partially supported by RFBR Grant No 18-29-10013.

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Authors and Affiliations

  1. Institute of Control Sciences of Russian Academy of Sciences, Moscow, Russia

    Anna Duyunova, Valentin V. Lychagin & Sergey Tychkov

Authors
  1. Anna Duyunova
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  2. Valentin V. Lychagin
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  3. Sergey Tychkov
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Corresponding author

Correspondence to Sergey Tychkov .

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Editors and Affiliations

  1. Baltic Institute of Mathematics, Warszawa, Poland

    Maria Ulan

  2. Baltic Institute of Mathematics, Warszawa, Poland

    Eivind Schneider

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Duyunova, A., Lychagin, V.V., Tychkov, S. (2021). Differential Invariants for Flows of Fluids and Gases. In: Ulan, M., Schneider, E. (eds) Differential Geometry, Differential Equations, and Mathematical Physics. Tutorials, Schools, and Workshops in the Mathematical Sciences . Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-63253-3_6

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