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

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

2003-06-04

arxiv.org/abs/math/0306075v1

Mathematics

Probability

Scientific paper

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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