A probabilistic representation for the vorticity of a 3D viscous fluid and for general systems of parabolic equations

B. Busnello; F. Flandoli; M. Romito

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A probabilistic representation for the vorticity of a 3D viscous fluid and for general systems of parabolic equations

B. Busnello·F. Flandoli·M. Romito

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Abstract

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 3D viscous fluid (described by the Navier-Stokes equations) is carefully analysed, and a theorem of local existence and uniqueness is proved.

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B. Busnello, F. Flandoli, M. Romito. 2003-06-04. A probabilistic representation for the vorticity of a 3D viscous fluid and for general systems of parabolic equations. https://arxiv.org/abs/math/0306075

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