Claude-Louis Navier

Claude-Louis Navier was a French engineer and physicist who in 1822 derived the equations of motion for viscous fluids, now known as the Navier–Stokes equations. He modified Euler's equations by adding a term accounting for internal friction (viscosity) and assumed a linear relationship between stresses and strain rates. These equations became the foundation of fluid dynamics, describing the flow of liquids and gases across an extremely wide range of conditions—from water flow in pipes to atmospheric processes. They underlie the modern analysis of the existence and smoothness problem, including the question of possible blow-up in finite time. Navier also contributed to the theory of elasticity, formulating the equilibrium and motion equations for elastic bodies, and to structural mechanics—a method for calculating beams bears his name. However, for the topic at hand, the key contribution is precisely the derivation of the equations of motion for viscous fluids, which became the starting point for all subsequent research, including the work of Leray, Hopf, and Ladyzhenskaya.