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

@article{Koide2011NavierStokesGA, title={Navier-Stokes, Gross-Pitaevskii and Generalized Diffusion Equations using Stochastic Variational Method}, author={Tomoi Koide and Takeshi Kodama}, journal={arXiv: Statistical Mechanics}, year={2011} }

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…

## 24 Citations

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We discuss the nonrelativistic limit of the relativistic Navier-Fourier-Stokes (NFS) theory. The next-to-leading order relativistic corrections to the NFS theory for the Landau-Lifshitz fluid are…

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- PhysicsPhysics Letters A
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Abstract The generalized uncertainty relation applicable to quantum and stochastic systems is derived within the stochastic variational method. This relation not only reproduces the well-known…

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