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.
Citation:
S. V. Meleshko, V. V. Pukhnachev, “One class of partially invariant solutions of the Navier–Stokes equations”, Prikl. Mekh. Tekh. Fiz., 40:2 (1999), 24–33; J. Appl. Mech. Tech. Phys., 40:2 (1999), 208–216
\Bibitem{MelPuk99}
\by S.~V.~Meleshko, V.~V.~Pukhnachev
\paper One class of partially invariant solutions of the Navier--Stokes equations
\jour Prikl. Mekh. Tekh. Fiz.
\yr 1999
\vol 40
\issue 2
\pages 24--33
\mathnet{http://mi.mathnet.ru/pmtf3051}
\elib{https://elibrary.ru/item.asp?id=28814906}
\transl
\jour J. Appl. Mech. Tech. Phys.
\yr 1999
\vol 40
\issue 2
\pages 208--216
\crossref{https://doi.org/10.1007/BF02468516}
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