25 citations · 119 across the 42 of their papers we have counts for
17 papers · 1 filter
Natural differential invariants and equivalence of third order nonlinear differential operators
Valentin Lychagin, Valeriy Yumaguzhin
We give a description of the field of rational natural differential invariants for a class of nonlinear differential operators of the third order on a two dimensional manifold and…
Quotient of the Euler system on one class of curves
Anna Duyunova, Valentin Lychagin, Sergey Tychkov
We consider the Euler system describing a one-dimensional inviscid flows in space along curves of a certain class. Using differential invariants for the Euler system, we obtain its…
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…
On Higher Order Structures in Thermodynamics
Valentin Lychagin, Mikhail Roop
We present the development of the approach to thermodynamics based on measurement. First of all, we recall that considering classical thermodynamics as a theory of measurement of e…
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)…