The Navier-Stokes equations represent a cornerstone of fluid dynamics, providing a mathematical framework to describe the motion of viscous fluids. These nonlinear partial differential equations ...

A $1 million prize awaits anyone who can show where the math of fluid flow breaks down. With specially trained AI systems, ...

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Turbulent times This visualization of fluid flow was made using laser-induced fluorescence. (Courtesy: C Fukushima and J Westerweel/Technical University of Delft/CC BY 3.0) The Navier–Stokes partial ...

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 From Quanta Magazine (find original ...

Partial differential equations can describe everything from planetary motion to plate tectonics, but they’re notoriously hard to solve. Unless you’re a physicist or an engineer, there really isn’t ...

Two mathematicians prove that under certain extreme conditions, the Navier-Stokes equations output nonsense. The Navier-Stokes equations capture in a few succinct terms one of the most ubiquitous ...