Thursday, January 17, 2013

1301.3586 (Vladimir V. Kulish et al.)

Exact solutions to the Navier-Stokes equation for an incompressible flow
from the interpretation of the Schroedinger wave function

Vladimir V. Kulish, Jose L. Lage
The existence of the velocity potential is a direct consequence from the derivation of the continuity equation from the Schroedinger equation. This implies that the Cole-Hopf transformation is applicable to the Navier-Stokes equation for an incompressible flow and allows reducing the Navier-Stokes equation to the Einstein-Kolmogorov equation, in which the reaction term depends on the pressure. The solution to the resulting equation, and to the Navier-Stokes equation as well, can then be written in terms of the Green's function of the heat equation and is given in the form of an integral mapping. Such a form of the solution makes bifurcation period doubling possible, i.e. solutions to transition and turbulent flow regimes in spite of the existence of the velocity potential.
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