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 ...

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

The currents of the oceans, the roiling surface of the sun, and the clouds of smoke billowing off a forest fire—all are ...

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 ...

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 ...

The irregular, swirling motion of fluids we call turbulence can be found everywhere, from stirring in a teacup to currents in ...

Scientific progress is not usually straightforward. Researchers pursue and abandon lines of inquiry. Results languish. Theories take decades to cohere. But sometimes the accumulation of scientific ...

The famed Navier-Stokes equations can lead to cases where more than one result is possible, but only in an extremely narrow set of situations. For nearly two centuries, all kinds of researchers ...

Mathematicians have suspected for years that under specific circumstances, the Euler equations fail. But they've been unable to identify an exact scenario in which this failure occurs. Until now. The ...