STOCHASTIC CASCADES APPLIED TO THE NAVIER-STOKES EQUATIONS

In this paper a representation of the Fourier transform of solutions to the Navier-Stokes Equations are obtained in terms of a stochastic recursion generated by a branching random walk. The notion of majorizing kernel is introduced and used to study regularity and existence of solutions of the Navier-Stokes equations. Similar representation of solutions to other equations are also discussed and its corresponding multiplicative recursion in the physical space are presented. This is joint work with R. Bhattacharya, L. Chen, S. Dobson, R. Guenther, C. Orum and E. Waymire.