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Navier-Stokes equations

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The Map of Mathematics

February 13, 2020

Explore our surprisingly simple, absurdly ambitious and necessarily incomplete guide to the boundless mathematical universe.

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fluid dynamics

Mathematicians Prove Universal Law of Turbulence

February 4, 2020

By exploiting randomness, three mathematicians have proved an elegant law that underlies the chaotic motion of turbulent systems.

Abstractions blog

For Fluid Equations, a Steady Flow of Progress

January 13, 2020

A startling experimental discovery about how fluids behave started a wave of important mathematical proofs.

Animation of two rings of fluid approaching each other and colliding.
fluid dynamics

Famous Fluid Equations Spring a Leak

December 18, 2019

Researchers have spent centuries looking for a scenario in which the Euler fluid equations fail. Now a mathematician has finally found one.

Art for "The Trouble With Turbulence"
In Theory

The Trouble With Turbulence

January 28, 2019

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

June 27, 2018

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.

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Abstractions blog

What Makes the Hardest Equations in Physics So Difficult?

January 16, 2018

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

December 21, 2017

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

mathematical physics

Famous Fluid Equations Are Incomplete

July 21, 2015

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