Phenomenological description of two-velocity media with relaxing tangential stresses

Dorovskii, V. N.; Perepechko, Yury

doi:10.1007/bf00851737

Cited by 19 publications

(7 citation statements)

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“…We have used a method of obtaining the dynamic equations which, in view of the nonrelativistic character of motions of a continuous medium and of the relativistic Maxwell equations, represents a combination of the variational principle in the form offered in [26,27] and of the requirement according to which the balance equation for the total energy-momentum tensor of a plasma-like medium and of the magnetic field should be satisfied. (Note that the requirement of satisfaction of the conservation laws, in particular, the energy balance equation, since the Landau pioneering work on the theory of superfluidity of helium II [50,51], is widely used to construct continuous models of quantum [37,[52][53][54] and classical [55][56][57] multivelocity continua.) The use of the base variational equation 2has allowed us to obtain a gauge-covariant system of the dynamic equations (129)-(131) and conditions at strong discontinuities (179)-(182).…”

Section: Discussionmentioning

confidence: 99%

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The gauge-invariant dynamic equations for current-carrying plasma-like media with topological defects

Volkov¹

1997

J. Phys. A: Math. Gen.

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A closed set of the gauge-invariant dynamic equations for a current-carrying plasmalike medium with dislocation-type and disclination-type topological defects together with the conditions at strong discontinuities is obtained using the variational principle and discussed. The dislocation and disclination fields, which compensate the non-homogeneity of the action of the gauge group G = SO(3) T (3), are described in the present theory by inexact external differential forms. The set of the Cartan structural equations for these forms has a direct correlation with the continuity equations for topological defects. The integrability conditions for the equations describing the dynamics of topological defects are obtained. It is shown that the integrability condition for the equation for disclination fields is equivalent to the balance equation for the angular momentum of the plasma-like medium together with the magnetic field. This condition is degenerated in the requirement of symmetry of the total stress tensor in the case of lack of topological defects. It is also shown that the total tensor of an energy-momentum of the plasma-like medium and of the magnetic field satisfies the balance equation.

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Section: Discussionmentioning

confidence: 99%

“…where m is the mass of a free electron. Differentiating equation (56), it is possible to obtain an expression for the momentum through which the invariant quasi-momentum of the conduction electrons in a deformable lattice is expressed (we take this expression as its definition):…”

Section: 21mentioning

confidence: 99%

The gauge-invariant dynamic equations for current-carrying plasma-like media with topological defects

Volkov¹

1997

J. Phys. A: Math. Gen.

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“…Then from the continuity equation (1) Let us consider the equations with the number i = m = 2 in the system (7), (8):…”

Section: First a Priori Estimatementioning

confidence: 99%

“…A survey of possible formulations of the model and known results can be found in [5], [6]. Related multi-velocity models are discussed in [7], [8], [9], [10], [11]. As the first results on the solvability of multifluid models in the multidimensional case (but in approximate formulations), we can indicate [12], [13], [14].…”

Section: Introductionmentioning

confidence: 99%

Global Unique Solvability of the Initial-Boundary Value Problem for the Equations of One-Dimensional Polytropic Flows of Viscous Compressible Multifluids

Mamontov

Prokudin

2019

J. Math. Fluid Mech.

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“…The method consists in the following: the requirement of the fullfillment of balance laws of mass, energy etc., complemented by the Galilean relativity principle and the Gibbs thermodynamic identity fully determines the governing equations of motion. Recently this approach was applied to classical fluids (two-velocity hydrodynamics) by Dorovsky & Perepechko [13], Roberts & Loper [14], Shugrin [15]. The method does not take into account the geometrical characteristics of the mixture components: the volume concentrations, sizes of particles etc.…”

Section: Introductionmentioning

confidence: 99%

Untitled

1998

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One derives the governing equations and the Rankine-Hugoniot conditions for a mixture of two miscible fluids using an extended form of Hamilton's principle of least action. The Lagrangian is constructed as the difference between the kinetic energy and a potential depending on the relative velocity of components. To obtain the governing equations and the jump conditions one uses two reference frames related with the Lagrangian coordinates of each component. Under some hypotheses on flow properties one proves the hyperbolicity of the governing system for small relative velocity of phases. Sommario. Le equazioni di governo e le condizioni di Rankine-Hugoniot sono derivate per una miscela di due fluidi miscibili usando una formulazione estesa del principio di minima azione di Hamilton. La Lagrangianaè costruita come differenza tra energia cinetica e potenziale dipendente dalla velocità relativa dei componenti. Per ottenere le equazioni di governo e le condizioni di salto si usano due sistemi di riferimento collegati alle coordinate Lagrangiane di ciascun componente. Nelle stesse ipotesi sulle propretà di flusso si prova l'iperbolicità del sistema per piccole velocità relative delle fasi.

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Phenomenological description of two-velocity media with relaxing tangential stresses

Cited by 19 publications

References 1 publication

The gauge-invariant dynamic equations for current-carrying plasma-like media with topological defects

The gauge-invariant dynamic equations for current-carrying plasma-like media with topological defects

Global Unique Solvability of the Initial-Boundary Value Problem for the Equations of One-Dimensional Polytropic Flows of Viscous Compressible Multifluids

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