What do the Navier-Stokes equations mean?

The Navier–Stokes equations are nonlinear partial differential equations describing the motion of fluids. Due to their complicated mathematical form they are not part of secondary school education. A detailed discussion of fundamental physics—the conservation of mass and Newton’s second law— may, however, increase the understanding of the behaviour of fluids. Based on these principles the Navier–Stokes equations can be derived. This article attempts to make these equations available to a wider readership, especially teachers and undergraduate students. Therefore, in this article a derivation restricted to simple differential calculus is presented. Finally, we try to give answers to the questions ‘what is a fluid?’ and ‘what do the Navier–Stokes equations mean?’. Keywords: