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Navier-Stokes equations

Art for "The Trouble With Turbulence"
In Theory

The Trouble With Turbulence

Turbulence is everywhere, yet it is one of the most difficult concepts for physicists to understand.

Photo of Jupiter for "Mathematicians Tame Turbulence in Flattened Fluids"
fluid dynamics

Mathematicians Tame Turbulence in Flattened Fluids

By squeezing fluids into flat sheets, researchers can get a handle on the strange ways that turbulence feeds energy into a system instead of eating it away.

Photo of smoke
Abstractions blog

What Makes the Hardest Equations in Physics So Difficult?

The Navier-Stokes equations describe simple, everyday phenomena, like water flowing from a garden hose, yet they provide a million-dollar mathematical challenge.

Simulation of Kelvin-Helmholz Instability
fluid dynamics

Mathematicians Find Wrinkle in Famed Fluid Equations

Two mathematicians prove that under certain extreme conditions, the Navier-Stokes equations output nonsense.

mathematical physics

Famous Fluid Equations Are Incomplete

A 115-year effort to bridge the particle and fluid descriptions of nature has led mathematicians to an unexpected answer.

Mathematics

For Persi Diaconis’ Next Magic Trick …

A mathematician who has analyzed card shuffling for decades is tackling one final nemesis: “smooshing.”

Submerged turbulent jet
Mathematics

A Fluid New Path in Grand Math Challenge

A daring speculation offers a potential way forward in one of the great unsolved problems of mathematics: the behavior of the Navier-Stokes equations for fluid flow.