Symmetries and Differential Invariants for Inviscid Flows on a Curve

  title={Symmetries and Differential Invariants for Inviscid Flows on a Curve},
  author={Anna Duyunova and Valentin V. Lychagin and Sergey Tychkov},
  journal={arXiv: Mathematical Physics},
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 thermodynamic states is given. 
Symmetry classification of viscid flows on space curves
Quotient of the Euler system on one class of curves
Quotients of Euler Equations on Space Curves
Using virial expansion of the Planck potential, the quotient equation for the Euler system describing a one-dimensional gas flow on a space curve is reduced to a series of systems of ordinary differential equations (ODEs).
Quotients of Navier–Stokes equation on space curves
A Navier–Stokes system on a curve is discussed. The quotient equation for this system is found. The quotient is used to find some solutions of Navier–Stokes system. Using virial expansion of the


Differential Invariants for Flows of Fluids and Gases
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
Global Lie–Tresse theorem
We prove a global algebraic version of the Lie–Tresse theorem which states that the algebra of differential invariants of an algebraic pseudogroup action on a differential equation is generated by a
Continuum mechanics of media with inner structures
An Introduction to Fluid Dynamics
Keywords: dynamique des : fluides Reference Record created on 2005-11-18, modified on 2016-08-08
Symmetries and differential invariants for inviscid flows on a curve
  • Lobachevskii Journal of Mathematics, 2020,
  • 2020
The Differential Geometry Package (2016)
  • Downloads. Paper 4.
  • 2016