A PROBABILISTIC REPRESENTATION FOR THE VORTICITY OF A THREE-DIMENSIONAL VISCOUS FLUID AND FOR GENERAL SYSTEMS OF PARABOLIC EQUATIONS

Barbara Busnello; Franco Flandoli; Marco Romito

doi:10.1017/S0013091503000506

Abstract

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A probabilistic representation formula for general systems of linear parabolic equations, coupled only through the zero-order term, is given. On this basis, an implicit probabilistic representation for the vorticity in a three-dimensional viscous fluid (described by the Navier–Stokes equations) is carefully analysed, and a theorem of local existence and uniqueness is proved. The aim of the probabilistic representation is to provide an extension of the Lagrangian formalism from the non-viscous (Euler equations) to the viscous case. As an application, a continuation principle, similar to the Beale–Kato–Majda blow-up criterion, is proved.

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A PROBABILISTIC REPRESENTATION FOR THE VORTICITY OF A THREE-DIMENSIONAL VISCOUS FLUID AND FOR GENERAL SYSTEMS OF PARABOLIC EQUATIONS

Abstract

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This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Article contents

A PROBABILISTIC REPRESENTATION FOR THE VORTICITY OF A THREE-DIMENSIONAL VISCOUS FLUID AND FOR GENERAL SYSTEMS OF PARABOLIC EQUATIONS

Abstract

Keywords

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