Navier-Stokes equations

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

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

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

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

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

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.

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

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

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