From Navier to Stokes: Commemorating the Bicentenary of Navier’s Equation on the Lay of Fluid Motion

Abstract

The article presents a summarised history of the equations governing fluid motion, known as the Navier–Stokes equations. It starts with the work of Castelli, who established the continuity equation in 1628. The determination of fluid flow resistance was a topic that involved the brightest minds of the 17th and 18th centuries. Navier’s contribution consisted of the incorporation of molecular attraction effects into Euler’s equation, giving rise to an additional term associated with resistance. However, his analysis was not the only one. This continued until 1850, when Stokes firmly established the boundary conditions that must be applied to the differential equations of motion, specifically stating the non-slip condition of the fluid in contact with a solid surface. With this article, the author wants to commemorate the bicentennial of the publication of “Sur les Lois du Mouvement des Fluides” by Navier in the Mémoires de l’Académie Royale des Sciences de l’Institut de France.

Keywords

• Navier–Stokes equation
• fluid flow resistance
• viscosity
• non-slip boundary condition