Duality, vector advection and the Navier-Stokes equations

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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.
Original languageEnglish
Pages (from-to)53-93
Number of pages41
JournalDynamics of Partial Differential Equations
Issue number1
Publication statusPublished - 1 Mar 2009


  • Fluid Dynamics,
  • Stochastic Analysis
  • Navier-Stokes equations,
  • Feynman Kac formula,
  • vector advection.

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