A variational principle for the Navier-Stokes equation (Q789613)

This paper presents an interesting variational principle combined with the probabilistic idea for the motion of incompressible viscous fluids. To overcome the difficulty arising from the dissipative terms in the Navier-Stokes equations, the author improves the stochastic calculus of variations, proposed by the same author, in such a way that the Navier- Stokes flow of incompressible viscous fluid is characterized as a volume preserving diffusion process which makes the total energy of the fluid stationary under a certain class of stochastic variations.