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A fresh look at the Navier-Stokes equation and the phenomenon of turbulence

Last modified: 2023-05-15

#### Abstract

Although the Navier-Stokes equation was written down in the 19th century, our understanding of it remains minimal. It seems that the time is ripe to try new approaches when treating the Navier-Stokes equation. This paper is an attempt to offer a new look at the equation governing fluid motion. In particular, it is shown that the Navier-Stokes equation can be derived and then treated in the same way as the heat equation with a nonlinear source term. Hence, its global solution is in the form of the Poincaré integral mapping, which allows chaotic behaviour (turbulence).