Random diffeomorphisms and integration of the classical Navier-Stokes equations
The author employs stochastic flows in order to obtain implicit representations for solutions of the Navier-Stokes equation for an incompressible viscous fluid in a smooth manifold which is isometrically embedded in the Euclidean space. Among technical tools are the Itô formula for diffusions on differential forms and gauge theoretical consideration. The results are viewed as an extension to smooth manifolds of the random vertex method of computational fluid dynamics.
scientific article; zbMATH DE number 1786197
scientific article