Journal of Vibration Testing and System Dynamics 7(1) (2023) 39--47 | DOI:10.5890/JVTSD.2023.03.006

V.V. Vedenyapin, N.N. Fimin, A.A. Russkov, M.Yu. Voronina

Keldysh Institute of Applied Mathematics of RAS, Moscow, Miusskaya square 4, Russian Federation

Abstract

Of the Maxwell and Einstein equations in the framework of the Vlasov--Maxwell--Einstein equations from the classical, but more general principle of least action. The resulting derivation of the Vlasov--type equations gives the Vlasov--Einstein equations different from those proposed earlier. A method is proposed for the transition from kinetic equations to hydrodynamic--type equations. In the case of Hamiltonian mechanics, the transition to the Hamilton--Jacobi equation from the hydrodynamic consequences of the Liouville equation is possible, as was done already in quantum mechanics. Thus, in the nonrelativistic case, we obtain the Milne--McCrea{--type} solutions.

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