Duality, vector advection and the Navier-Stokes equations (Q843082)

The authors review the classical result of Serrin on the existence of strong solutions to the Navier-Stokes equation. They consider three-dimensional vector advection equation and show some special properties for it, e.g. self-duality. They deduce the Feynman-Kac formula for the solution of the advection equation and show that the formula is not unique. As a consequence they show the existence of flows along which the vorticity is conserved.