Duality, vector advection and the Navier-Stokes equations

TY - JOUR

T1 - Duality, vector advection and the Navier-Stokes equations

AU - Brzezniak, Zdzislaw

AU - Neklyudov, Misha

PY - 2009/3/1

Y1 - 2009/3/1

N2 - 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.

AB - 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.

KW - Fluid Dynamics,

KW - Stochastic Analysis

KW - Navier-Stokes equations,

KW - Feynman Kac formula,

KW - vector advection.

UR - http://www.scopus.com/inward/record.url?scp=66849110736&partnerID=8YFLogxK

M3 - Article

VL - 6

SP - 53

EP - 93

JO - Dynamics of Partial Differential Equations

JF - Dynamics of Partial Differential Equations

IS - 1

ER -