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

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 ...

Solving Navier-Sokes equations are popular because they describe the physics of in a number of areas of interest to scientists and engineers. By solving these equations, the flow velocity can be ...

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 ...

You're currently following this author! Want to unfollow? Unsubscribe via the link in your email. Follow Andy Kiersz Every time Andy publishes a story, you’ll get an alert straight to your inbox!

The days of yacht designers building scaled down models of sail boats and then bobbing them in tanks of water—to see how sleekly they moved—ended decades ago. Computers now do the same job with more ...

This is a preview. Log in through your library . Abstract We consider in this paper a hyperbolic quasilinear version of the Navier-Stokes equations in three space dimensions, obtained by using ...

Let u be a weak solution of the Navier-Stokes equations in a smooth domain Ω ⊆ ℝ3 and a time interval [0,T), 0 < T ≤ ∞, with initial value u0, and vanishing external force. As is well known, global ...

Fourier's well-known heat equation, introduced in 1822, describes how temperature changes in space and time when heat flows through a material. In general, this formulation works well to describe heat ...

Rose Yu has a plan for how to make AI better, faster and smarter — and it’s already yielding results. In math and computer science, researchers have long understood that some questions are ...