Intuitive

• What Makes the Hardest Equations in Physics So Difficult? (Quanta Magazine)
• Mathematicians Find Wrinkle in Famed Fluid Equations (Quanta Magazine)

Concrete

Abstract

Why is it interesting?

The Navier-Stokes equations describe one of the most ubiquitous features of our world: the flow of fluids. They are used to study ocean currents, the turbulence in the wave of an airplane or the flow of blood.

In addition, they are mathematically extremely interesting and there is a Millennium Prize Problem with $1 million reward for the first person who can prove rigorously that solutions exist and answer the question if they are unique.

FAQ

What makes the Navier-Stokes equations so difficult?

See the discussion here.

Why are Navier-Stokes equations needed?

https://physics.stackexchange.com/questions/45839/why-are-navier-stokes-equations-needed