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Symmetries and conservation laws of Navier-Stokes equations. (English) Zbl 0682.35086
By direct calculations it is proved that the algebra of all symmetries of Navier-Stokes equations consists only of the contact symmetries. It is also proved that the space of all conservation laws of these equations is generated by a “generalised impulse”, the impulse moment and the quantity of substance conservation laws.
Reviewer: V.N.Gusyatnikova

35Q30Stokes and Navier-Stokes equations
35Q99PDE of mathematical physics and other areas
35A30Geometric theory for PDE, characteristics, transformations
35L65Conservation laws
Full Text: DOI
[1] PoochnachevV. V.: Group properties of Navier-Stokes equations in the flat case,J. Appl. Mech. Tech. Phys. 1 (1960), 83-90. (in Russian)
[2] BytevV. O.: Group properties of Navier-Stokes equations,Numerical Methods of the Solid Medium,3 (1972), N. 3, Novosibirsk, Vych. Centr. Sibir. Otd. Acad. Nauk SSSR, pp. 13-17. (in Russian)
[3] KrasilshchikI. S., LychaginV. V., and VinogradovA. M.:Geometry of Jet Spaces and Nonlinear Partial Differential Equations, Gordon and Breach, New York, 1986.
[4] VinogradovA. M.: Symmetries and conservation laws of partial differential equations: Basic notions and results,Acta. Appl. Math. 15 (1989), 3-21. · Zbl 0692.35002 · doi:10.1007/BF00131928
[5] VinogradovA. M.: Local symmetries and conservation laws,Acta Appl. Math. 2 (1984), 21-78. · Zbl 0534.58005 · doi:10.1007/BF01405491
[6] VinogradovA. M.: TheC-spectral sequence, Lagrangian formalism and conservation laws. 1. The linear theory; 2. The nonlinear theory,J. Math. Anal. Appl. 100 (1984), 1-129. · Zbl 0548.58014 · doi:10.1016/0022-247X(84)90071-4