A 115-year effort to bridge the particle and fluid descriptions of nature has led mathematicians to an unexpected answer. In 1900, the great mathematician David Hilbert presented a list of 23 unsolved ...

The Navier-Stokes equations capture in a few succinct terms one of the most ubiquitous features of the physical world: the flow of fluids. The equations, which date to the 1820s, are today used to ...

The following is an extract from our Lost in Space-Time newsletter. Each month, we hand over the keyboard to a physicist or mathematician to tell you about fascinating ideas from their corner of the ...

When a fluid is in motion, it must move in such a way that mass is conserved. To see how mass conservation places restrictions on the velocity field, consider the steady flow of fluid through a duct ...

We continue our exploration of fluids and fluid dynamics. We continue our exploration of fluids and fluid dynamics. How do fluids act when they're in motion? How does pressure in different places ...

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 ...