On Landau's Solutions of the Navier-Stokes Equations
Analysis of PDEs
2012-12-04 v2
Abstract
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. We also discuss the situation for general dimension.
Cite
@article{arxiv.math/0604550,
title = {On Landau's Solutions of the Navier-Stokes Equations},
author = {Vladimir Sverak},
journal= {arXiv preprint arXiv:math/0604550},
year = {2012}
}
Comments
16 pages, an extension of the previous version, includes now also results for general dimension