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 ...

The axisymmetric Navier-Stokes equations describe the motion of incompressible fluids under the assumption of rotational symmetry around a fixed axis. This reduction in dimensional complexity retains ...

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 ...

Two mathematicians prove that under certain extreme conditions, the Navier-Stokes equations output nonsense. The Navier-Stokes equations capture in a few succinct terms one of the most ubiquitous ...

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 ...

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 ...

This is a preview. Log in through your library . Abstract First part of this paper presents an overview of some low Mach flow approximations to the compressible Navier-Stokes equations. Their ...

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 ...

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 ...