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 ...

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 ...

For centuries, mathematicians have sought to understand and model the motion of fluids. The equations that describe how ripples crease the surface of a pond have also helped researchers to predict the ...

Stochastic fluid dynamics extends classical fluid mechanics by incorporating randomness and uncertainty directly into the governing equations. This approach utilises stochastic differential equations ...

Fluid dynamics, a cornerstone of applied mathematics and engineering, investigates the behaviour of fluids in motion. Within this broad field, active scalar equations play a pivotal role by ...

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 ...

points 1 and 2 lie on a streamline, the fluid has constant density, the flow is steady, and there is no friction. Although these restrictions sound severe, the Bernoulli equation is very useful, ...

For decades, researchers have been using equations derived in the mid-1970s for a variety of fluid applications involving inks, foams, and bubbles, among other uses. These fundamental fluid equations ...