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, ...

As we celebrate the International Year of Quantum Science and Technology (IYQ) in 2025, we look back on a century of quantum mechanics—a field that has fundamentally changed the way we understand ...

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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 ...

Jim Denier receives funding from the Australian Research Council. MILLENNIUM PRIZE SERIES: The Millennium Prize Problems are seven mathematics problems laid out by the Clay Mathematics Institute in ...

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 ...

Partial differential equations can describe everything from planetary motion to plate tectonics, but they’re notoriously hard to solve. Ms Tech | Science Photo Library via AP Unless you’re a physicist ...