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Stochastic variational derivations of the Navier-Stokes equation

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Abstract

Stochastic calculus of variations in terms of sample paths is shown to be equivalent to ordinary calculus of variations in terms of local drift fields when applied to Markov processes. This equivalence enables us to derive the Navier-Stokes equation directly through a variational principle.

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Authors and Affiliations

  1. Department of Physics, Faculty of Science, Kyoto University, 606, Kyoto, Japan

    T. Nakagomi

  2. Département de Physique Théorique, Université de Genève, CH-1211, Genève 4, Switzerland

    K. Yasue & J. -C. Zambrini

Authors
  1. T. Nakagomi
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  2. K. Yasue
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  3. J. -C. Zambrini
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Additional information

Partially supported by the Swiss National Science Foundation.

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Nakagomi, T., Yasue, K. & Zambrini, J.C. Stochastic variational derivations of the Navier-Stokes equation. Lett Math Phys 5, 545–552 (1981). https://doi.org/10.1007/BF00408137

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  • DOI: https://doi.org/10.1007/BF00408137

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