← Glossary Term
Navier-Stokes
The equations that describe how fluids like air and water move, and one of mathematics' most famous unsolved problems.
The Navier-Stokes equations describe how liquids and gases flow, from water in a pipe to wind around a plane. Engineers use them every day to simulate weather, aircraft and blood flow.
The famous open question is mathematical: nobody has proved that the equations always have smooth, well-behaved solutions in three dimensions. There is a million-dollar prize for settling it, which is why any claimed AI-assisted proof gets intense scrutiny.
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