S. V. Meleshko, V. V. Pukhnachev, “One class of partially invariant solutions of the Navier–Stokes equations”, Prikl. Mekh. Tekh. Fiz., 1999, Volume 40, Issue 2,Pages <nobr>24

This article is cited in 39 papers

One class of partially invariant solutions of the Navier–Stokes equations

S. V. Meleshko^a, V. V. Pukhnachev^b

^a Institute of Theoretical and Applied Mechanics, Siberian Division, Russian Academy of Sciences, 630090, Novosibirsk
^b Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, 630090, Novosibirsk

Abstract: A family of partially invariant solutions of the Navier–Stokes equations of rank 2 and defect 2 is considered. These solutions describe the three-dimensional unsteady motions of a viscous incompressible fluid in which the vertical velocity component and the pressure are independent of the horizontal coordinates. In particular, they can be interpreted as flows in a horizontal layer, one boundary of which is the free surface.

UDC: 532.516

Received: 25.06.1998