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

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 ...

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 ...

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 ...

Virial coefficients are fundamental parameters in the statistical description of fluids, encapsulating the effects of molecular interactions on macroscopic thermodynamic properties. Through the virial ...