Probability Theory and Related Fields

, Volume 133, Issue 2, pp 267–298

A probabilistic representation of solutions of the incompressible Navier-Stokes equations in R3

  • Mina Ossiander
Article

DOI: 10.1007/s00440-004-0418-z

Cite this article as:
Ossiander, M. Probab. Theory Relat. Fields (2005) 133: 267. doi:10.1007/s00440-004-0418-z

Abstract

A new probabilistic representation is presented for solutions of the incompressible Navier-Stokes equations in R3 with given forcing and initial velocity. This representation expresses solutions as scaled conditional expectations of functionals of a Markov process indexed by the nodes of a binary tree. It gives existence and uniqueness of weak solutions for all time under relatively simple conditions on the forcing and initial data. These conditions involve comparison of the forcing and initial data with majorizing kernels.

Mathematics Subject Classification (2000)

Primary 35C15 60H30 Secondary 60J85 

Keywords

Tree-indexed Markov process Branching random walk Incompressible Navier-Stokes equations 

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Mina Ossiander
    • 1
  1. 1.Department of MathematicsOregon State UniversityUSA