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

Perhaps the oldest and most prominent of these equations, formulated by Leonhard Euler more than 250 years ago, describe the flow of an ideal, incompressible fluid: a fluid with no viscosity, or ...

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

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 ...

Dr. Julien's primary areas of research are in the dynamics and instability processes in geophysical and astrophysical fluid dynamics. These include turbulent fluid convection and the effects of ...

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 ...