An Exact Mapping from Navier-Stokes Equation to Schr\"{o}dinger Equation via Riccati Equation

In the present article we argue that it is possible to write down Schr\"{o}dinger representation of Navier-Stokes equation via Riccati equation. The proposed approach, while differs appreciably from other method such as what is proposed by R. M. Kiehn, has an advantage, i.e. it enables us extend further to quaternionic and biquaternionic version of Navier-Stokes equation, for instance via Kravchenko's and Gibbon's route. Further observation is of course recommended in order to refute or verify this proposition.