Abstract
We use forward–backward stochastic differential systems to study the solution of the Navier–Stokes- equation in any dimension. For the two dimensional Navier–Stokes- equation with space periodic boundary conditions, we derive a Feynman-Kac formula associated with the vorticity equation and prove the global existence and uniqueness of the solution in a Sobolev space. For the d dimensional () case, we prove the local existence and uniqueness of the solution in a Sobolev space.
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