Navier-Stokes, Gross-Pitaevskii and Generalized Diffusion Equations using Stochastic Variational Method

  title={Navier-Stokes, Gross-Pitaevskii and Generalized Diffusion Equations using Stochastic Variational Method},
  author={Tomoi Koide and Takeshi Kodama},
  journal={arXiv: Statistical Mechanics},
  • T. Koide, T. Kodama
  • Published 31 July 2011
  • Physics, Mathematics
  • arXiv: Statistical Mechanics
The stochastic variational method is applied to particle systems and continuum mediums. As the brief review of this method, we first discuss the application to particle Lagrangians and derive a diffusion-type equation and the Schr\"{o}dinger equation with the minimum gauge coupling. We further extend the application of the stochastic variational method to Lagrangians of continuum mediums and show that the Navier-Stokes, Gross-Pitaevskii and generalized diffusion equations are derived. The… 
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