On the uniqueness of the solution of the two-dimensional Navier-Stokes equation with a Dirac mass as initial vorticity
Analysis of PDEs
2007-05-23 v1 Mathematical Physics
math.MP
Abstract
We propose two different proofs of the fact that Oseen's vortex is the unique solution of the two-dimensional Navier-Stokes equation with a Dirac mass as initial vorticity. The first argument, due to C.E. Wayne and the second author, is based on an entropy estimate for the vorticity equation in self-similar variables. The second proof is new and relies on symmetrization techniques for parabolic equations.
Keywords
Cite
@article{arxiv.math/0410344,
title = {On the uniqueness of the solution of the two-dimensional Navier-Stokes equation with a Dirac mass as initial vorticity},
author = {Isabelle Gallagher and Thierry Gallay and Pierre-Louis Lions},
journal= {arXiv preprint arXiv:math/0410344},
year = {2007}
}
Comments
9 pages, no figure