On Landau's Solutions of the Navier-Stokes Equations

Details On Landau's Solutions of the Navier-Stokes Equations On Landau's Solutions of the Navier-Stokes Equations

2006-04-26

arxiv.org/abs/math/0604550v1

Mathematics

Analysis of PDEs

7 pages

Scientific paper

In 1944 L.D.Landau calculated a very interesting family of explicit solutions of the steady-state 3d Navier-Stokes equations. The solutions are derived under certain assumptions of symmetry, which reduce the Navier-Stokes equations to a system of ODEs. We investigate what happens when some of the symmetry conditions are dropped (and we have to deal with PDEs). Implications of these calculations for more general classes of solutions are also discussed.

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