The Navier-Stokes equations represent a cornerstone of fluid dynamics, providing a mathematical framework to describe the motion of viscous fluids. These nonlinear partial differential equations ...

Finite Element Methods (FEM) have emerged as a pivotal computational tool in the simulation of incompressible flows and the Navier-Stokes equations. By discretising the domain, these techniques offer ...

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 ...

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 ...

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The Navier-Stokes equations describe simple, everyday phenomena, like water flowing from a garden hose, yet they provide a million-dollar mathematical challenge. Physics contains equations that ...

Turbulent times This visualization of fluid flow was made using laser-induced fluorescence. (Courtesy: C Fukushima and J Westerweel/Technical University of Delft/CC BY 3.0) The Navier–Stokes partial ...

Partial differential equations can describe everything from planetary motion to plate tectonics, but they’re notoriously hard to solve. Unless you’re a physicist or an engineer, there really isn’t ...

Equations are the bedrock of science, expressing how numbers or physical properties relate at a fundamental level. Without equations, most of our technology would never have been invented. We may have ...

As we celebrate the International Year of Quantum Science and Technology (IYQ) in 2025, we look back on a century of quantum mechanics—a field that has fundamentally changed the way we understand ...