WE PRESENT THE RANDOM REPRESENTATIONS FOR THE NAVIER-STOKES VORTICITY EQUATIONS FOR AN INCOMPRESSIBLE FLUID IN A SMOOTH MANIFOLD WITH BOUNDARY AND REFLECTING BOUNDARY CONDITIONS FOR THE VORTICITY. WE SPECIALIZE OUR CONSTRUCTIONS TO R(n-1)xR+. WE EXTEND THESE CONSTRUCTIONS TO GIVE THE RANDOM REPRESENTATIONS FOR THE KINEMATIC DYNAMO PROBLEM OF MAGNETOHYDRODYNAMICS. WE CARRY OUT THESE INTEGRATIONS THROUGH THE APPLICATION OF THE METHODS OF STOCHASTIC DIFFERENTIAL GEOMETRY, I.E. THE GAUGE THEORY OF DIFFUSION PROCESSES ON SMOOTH MANIFOLDS.
Symmetry reduction and exact solutions of the Navier-Stokes equations
Directional approach to spatial structure of solutions to the Navier-Stokes equations in the plane
Self-Similar Solutions with Elliptic Symmetry for the Compressible Euler and Navier-Stokes Equations in R^{N}
