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Navier-Stokes equations
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For Fluid Equations, a Steady Flow of Progress
A startling experimental discovery about how fluids behave started a wave of important mathematical proofs.
Famous Fluid Equations Spring a Leak
Researchers have spent centuries looking for a scenario in which the Euler fluid equations fail. Now a mathematician has finally found one.
The Trouble With Turbulence
Turbulence is everywhere, yet it is one of the most difficult concepts for physicists to understand.
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.
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.
Mathematicians Find Wrinkle in Famed Fluid Equations
Two mathematicians prove that under certain extreme conditions, the Navier-Stokes equations output nonsense.
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.
For Persi Diaconis’ Next Magic Trick …
A mathematician who has analyzed card shuffling for decades is tackling one final nemesis: “smooshing.”
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.