Differential Invariants for Flows of Fluids and Gases

@article{Duyunova2020DifferentialIF,
  title={Differential Invariants for Flows of Fluids and Gases},
  author={Anna Duyunova and Valentin V. Lychagin and Sergey Tychkov},
  journal={arXiv: Mathematical Physics},
  year={2020},
  pages={187-231}
}
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. 
Symmetries and Differential Invariants for Inviscid Flows on a Curve
Symmetries and the corresponding fields of differential invariants of the inviscid flows on a curve are given. Their dependence on thermodynamic states of media is studied, and a classification of
Quotient of the Euler system on one class of curves

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