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Mathematics

Fluid Dynamics and the Navier–Stokes Equations

Quick fact

The Navier–Stokes equations, formulated by Claude-Louis Navier and George Gabriel Stokes in the 19th century, remain one of the seven Clay Millennium Prize Problems: we do not yet know if they always have a smooth, global solution for 3D flows, a fact with a $1 million bounty.

Why this is interesting

The same equations that describe a calm river also describe the chaotic swirl of a typhoon. How can one set of equations capture all that motion—and why do we still not fully understand them?

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Fluid Dynamics and the Navier–Stokes Equations

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