Duality, Vector advection and the Navier-Stokes equations
Probability
2008-11-20 v3 Analysis of PDEs
Abstract
In this article we show that three dimensional vector advection equation is self dual in certain sense defined below. As a consequence, we infer classical result of Serrin of existence of strong solution of Navier-Stokes equation. Also we deduce Feynman-Kac type formula for solution of the vector advection equation and show that the formula is not unique i.e. there exist flows which differ from standard flow along which vorticity is conserved.
Keywords
Cite
@article{arxiv.0710.3401,
title = {Duality, Vector advection and the Navier-Stokes equations},
author = {Z. Brzezniak and M. Neklyudov},
journal= {arXiv preprint arXiv:0710.3401},
year = {2008}
}
Comments
51 pages; Some minor mistakes are corrected