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A probabilistic representation of solutions of the incompressible Navier-Stokes equations in R3
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  • Published: 06 June 2005

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

  • Mina Ossiander1 

Probability Theory and Related Fields volume 133, pages 267–298 (2005)Cite this article

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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.

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Authors and Affiliations

  1. Department of Mathematics, Oregon State University, USA

    Mina Ossiander

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  1. Mina Ossiander
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Ossiander, M. A probabilistic representation of solutions of the incompressible Navier-Stokes equations in R3. Probab. Theory Relat. Fields 133, 267–298 (2005). https://doi.org/10.1007/s00440-004-0418-z

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  • Received: 30 June 2004

  • Revised: 12 November 2004

  • Published: 06 June 2005

  • Issue Date: October 2005

  • DOI: https://doi.org/10.1007/s00440-004-0418-z

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Mathematics Subject Classification (2000)

  • Primary 35C15
  • 60H30
  • Secondary 60J85

Keywords

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