Navier-Stokes Equation by Stochastic Variational Method
Statistical Mechanics
2012-06-18 v2 High Energy Physics - Phenomenology
High Energy Physics - Theory
Nuclear Theory
Fluid Dynamics
Abstract
We show for the first time that the stochastic variational method can naturally derive the Navier-Stokes equation starting from the action of ideal fluid. In the frame work of the stochastic variational method, the dynamical variables are extended to stochastic quantities. Then the effect of dissipation is realized as the direct consequence of the fluctuation-dissipation theorem. The present result reveals the potential availability of this approach to describe more general dissipative processes.
Cite
@article{arxiv.1105.6256,
title = {Navier-Stokes Equation by Stochastic Variational Method},
author = {T. Koide and T. Kodama},
journal= {arXiv preprint arXiv:1105.6256},
year = {2012}
}
Comments
5 pages, no figure, discussions and references are added, errors in Sec. IV were corrected