<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Brzezniak, Zdzislaw</style></author><author><style face="normal" font="default" size="100%">Neklyudov, Misha</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Duality, vector advection and the Navier-Stokes equations</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamics of Partial Differential Equations</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">Fluid Dynamics</style></keyword><keyword><style  face="normal" font="default" size="100%">Stochastic Analysis</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2009</style></year><pub-dates><date><style  face="normal" font="default" size="100%">03/2009</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://intlpress.com/DPDE/journal/vol6/6-1/DPDE-6-1-A4-brzezniak.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">6</style></volume><pages><style face="normal" font="default" size="100%">53-93</style></pages><abstract><style face="normal" font="default" size="100%">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.</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><section><style face="normal" font="default" size="100%">53</style></section></record></records></xml>