Today is Claude-Louis Navier’s birthday

Claude-Louis Navier was born 10 February 1785 in Paris, France. He is famous of course for the Navier-Stokes equations named after him and George Gabriel Stokes. The Navier-Stokes describe the motion of viscous fluids and are derived by applying Newton’s Second Law (conservation of momentum) to the motion of a fluid. Most CFD codes solve a discrete form of the Navier-Stokes numerically.

Navier was an engineer and physicist and directed the construction of several bridges before becoming a professor of calculus and mechanics at the Ecole Polytechnique. He was the first to formulate the equations of viscous fluid motion, in 1827. (Stokes contribution, in 1845, was to use the concept of the coefficient of viscosity instead of writing the equations in terms of an unknown molecular function.)

In addition to his contributions to fluid mechanics, Navier is also known as the founder of modern structural analysis. He developed the first mathematically practical statement of the theory of elasticity and established that elastic modulus is a material property.

While the Navier-Stokes equations have been around for close to 200 years now, they are non-linear partial differential equations and fewer than 100 particular solutions have been found. They have only come into broad use with the development of modern computers and CFD techniques that can accurately approximate them.

However, there are still open questions related to the Navier-Stokes equations. Despite the fact that we rely heavily on them in CFD, there are no mathematical proofs that they have unique 3D solutions, or that if solutions exist, they do not contain singularities. This has been identified by the Clay Mathematics Institute as one of 7 Millennium Problems that are the deepest, most difficult questions in mathematics. (There is a $1,000,000 prize for the solution.)

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