Navier-Stokes equations

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.

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

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.