Navia

Navia guards a prize chest beside a swirling river. Inside is one question about smooth flows.

The Physics

The incompressible Navier–Stokes equations describe how water and air move. The Clay Millennium Prize question asks whether, in three dimensions, smooth initial flows always stay smooth, or whether a finite-time singularity can form.

ρ (∂u/∂t + (u·∇)u) = −∇p + μ ∇²u, ∇·u = 0

• ρ: density (kg/m³)
• u: flow velocity (m/s)
• t: time (s)
• p: pressure (Pa)
• μ: dynamic viscosity (Pa·s)
• ∇: spatial derivative (1/m)

The Clay Mathematics Institute announced the seven Millennium Prize Problems, each worth $1 million, on 24 May 2000.

On the shirt

Front: Navia, the pixel-art character, with the title. Back: the Navier–Stokes equations, the incompressibility condition, the smoothness question and the Clay source. Printed on a unisex tee.