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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67688A 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.ProbabilityAnalysis of PDEs76D05; 35A20A probabilistic representation for the vorticity of a 3D viscous fluid and for general systems of parabolic equationstext