Titlebook: Conservation Laws in Variational Thermo-Hydrodynamics; Stanislaw Sieniutycz Book 1994 Springer Science+Business Media Dordrecht 1994 Dissi

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,Physical significance of Nöther’s symmetries and extremum principles, on a set of the functions, the function on a set of the numbers. More precisely, let Q will be the set of functions; q, r, s …; then a functional A defined on Q is a mapping A: Q → R. which associates to each q ∈ Q a real number A(q). In general, the set of the functions may constitute any set of geometric objects, scalars, vectors, tensors, etc.

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Eulerian and Lagrangian descriptions of perfect fluids,bsystem with sufficiently large number of molecules to allow macroscopic definitions of thermo-hydrodynamic variables. Here we consider a single-component fluid with the density p, the specific entropy s, and the velocity . in the Eulerian coordinates. This fluid is called the perfect fluid if it do

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Conservation laws for given system of equations,roperties of solutions and to determine physical quantities which are constant in time. Therefore finding the conservation laws is an important problem, encountered in fluid mechanics and nonequilibrium thermodynamics of continua.

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