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Navier-Stokes Equation by Stochastic Variational Method
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.Comment: 5 pages, no figure, discussions and references are added, errors in
Sec. IV were correcte
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