• Navia Navier–Stokes Problem pixel-art physics T-shirt, white tee, front view

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Navia

The $1M Fluid Problem Physics

\[\rho\left(\frac{\partial \mathbf{u}}{\partial t} + (\mathbf{u}\cdot\nabla)\mathbf{u}\right) = -\nabla p + \mu\nabla^{2}\mathbf{u}\]
$29.99 USD
$29.99 USD
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Size guide S–5XL · inches

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.

Shipping calculated at checkout by destinationMade to order, ships in 2–5 business days

Details

Size & fitS–5XL

Unisex heavy cotton (Gildan 5000), classic fit.

SizeWidthLengthSleeve
S182815.1
M202916.5
L223018
XL243119.5
2XL263221
3XL283322.4
4XL303423.7
5XL323525

Zum Größenvergleich: Größe M ist 20 in (50.80 cm) breit, etwa 3.143 × 1034 Planck-Längen (lP = 1.616255 × 10−35 m). Ein Maßband geht schneller.

Measurements in inches, ±1.5 in tolerance.

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Shipping calculated at checkout by destination. Printed to order for you.

Delivery times & where we ship

Returns & replacements21 days

Every item is printed to order, so we can’t accept returns or exchanges for change of mind, or if you ordered the wrong size or colour.

Print defect, misprint, damage or the wrong item? We’ll send a free replacement, or a refund if you prefer. Report it within 21 days of delivery with a photo; no need to send it back.

Full refund & replacement policy

The physics

I guard a prize chest beside a swirling river. Inside is one question about smooth flows, and a million dollars.

The Navier–Stokes equations describe how water and air move: density times acceleration equals the push of pressure plus the drag of viscosity, with the fluid neither created nor destroyed. Written down in the nineteenth century, they predict breezes and turbulence. Yet one basic question stayed open: in three dimensions, does a smooth flow always stay smooth, or can a singularity form in a finite time?

The Clay Mathematics Institute made that a Millennium Prize Problem on 24 May 2000. In September 2026 a claimed resolution was announced, and Clay said the problem had “apparently been settled”. That claim is now under review under Clay's deliberately unhurried rules, and the prize has not been awarded. Until it is, my chest stays shut.

Equations

\[\rho\left(\frac{\partial \mathbf{u}}{\partial t} + (\mathbf{u}\cdot\nabla)\mathbf{u}\right) = -\nabla p + \mu\nabla^{2}\mathbf{u}\]
\[\nabla\cdot\mathbf{u} = 0\]
SymbolMeaningUnit
\(\rho\) fluid density (constant) \(\mathrm{kg/m³}\)
\(\mathbf{u}\) flow velocity \(\mathrm{m/s}\)
\(t\) time \(\mathrm{s}\)
\(p\) pressure \(\mathrm{Pa}\)
\(\mu\) dynamic viscosity \(\mathrm{Pa·s}\)
\(\nabla\) spatial derivative (gradient) operator \(\mathrm{1/m}\)

Sources

  1. Fefferman (2000) Existence and Smoothness of the Navier–Stokes Equation, Clay Mathematics Institute official problem description
  2. Clay Mathematics Institute (2026) Navier-Stokes Announcement, 11 September 2026
  3. Clay Mathematics Institute, Rules for the Millennium Prizes

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