On Landau ’ S Solutions of the Navier-stokes Equations

@inproceedings{verk2006OnL,
title={On Landau ’ S Solutions of the Navier-stokes Equations},
author={Vladimı́r {\vS}ver{\'a}k},
year={2006}
}

Vladimı́r Šverák

Published 2006

where u = (u1, . . . , un). The equations have a non-trivial scaling symmetry u(x) → λu(λx) and it is natural to try to find solutions which are invariant under this scaling. The simplest natural domain of definition for such solutions is R \ {0}. In this case, assuming that the solutions are smooth in R \ {0}, we are able to obtain a good classification of the invariant solutions in all dimensions. There are some interesting conclusions for the regularity theory as well as for the long… CONTINUE READING