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From stochastic processes to the hydrodynamic equations

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  • Beck, Christian
  • Roepstorff, Gert

Abstract

Starting from the Langevin equation for the (rescaled) position of a single particle in an incompressible liquid we derive an infinite hierarchy of hydrodynamic equations for suitably defined conditional expectations. Among them is the continuity equation, the Navier-Stokes equation, and the energy balance equation with Prandtl number Pr=1. Our approach uses a path integral formulation and the Fokker-Planck equation. The results demonstrate how the basic hydrodynamic equations arise from a stochastic independent particle model.

Suggested Citation

  • Beck, Christian & Roepstorff, Gert, 1990. "From stochastic processes to the hydrodynamic equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 165(2), pages 270-278.
  • Handle: RePEc:eee:phsmap:v:165:y:1990:i:2:p:270-278
    DOI: 10.1016/0378-4371(90)90195-X
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