This article is cited in 2 papers

Integrals of motion of an incompressible fluid occupying the entire space

V. V. Pukhnachev

Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk, 630090

Abstract: This paper studies integral relations to which the solutions of the Navier–Stokes equations or Euler equations satisfy in the case of fluids filling the entire three-dimensional space. The existence of these relations is due to a rapid decrease of the velocity field at infinity (but not too rapid in order that the required asymptotic forms are reproduced with time). Of special interest are the integrals of motion whose density depends quadratically on the velocities or their derivative with respect to the coordinates. Such integrals (conservation laws) for the Navier–Stokes equations were recently found by Dobrokhotov and Shafarevich. In the present paper, new conservation laws are obtained, which are quadratic in the derivatives of the velocity and lead to identities that link the averaged and pulsation characteristics of ree turbulent flows.

Keywords: Navier–Stokes equations, Euler equation, conservation laws.

UDC: 532.5

Received: 06.11.2003

 English version: Journal of Applied Mechanics and Technical Physics, 2004, 45:2, 167–171

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