English

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