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Thermodynamics of Viscous Flows on Surfaces
Anna Duyunova, Valentin Lychagin, Sergey Tychkov
In this paper, thermodynamics of a moving medium is considered. Main goal of this paper is to describe thermodynamics state equations and equations of co-existence manifolds of med…
On Dynamics and Thermodynamics of Moving Media
Anna Duyunova, Valentin Lychagin, Sergey Tychkov
In this paper recent results regarding generalized continuum mechanics on oriented Riemannian manifolds are reviewed and summarized. The mass, the momentum and the energy conservat…
Quotients of Navier--Stokes equation on space curves
Anna Duyunova, Valentin Lychagin, Sergey Tychkov
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…
Symmetry classification of viscid flows on space curves
Anna Duyunova, Valentin Lychagin, Sergey Tychkov
Symmetries and differential invariants of viscid flows with viscosity depending on temperature on a space curve are given. Their dependence on thermodynamic states of media is stud…
Continuum mechanics of media with inner structures
Anna Duyunova, Valentin Lychagin, Sergey Tychkov
We propose a geometrical approach to the mechanics of continuous media equipped with inner structures and give the basic (mass conservation, Navier-Stokes and energy conservation)…
Symmetries and Differential Invariants for Inviscid Flows on a Curve
Anna Duyunova, Valentin Lychagin, Sergey Tychkov
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 c…