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 ...

A huge mathematical breakthrough might have just been made, but a language barrier is slowing things down. New Scientist reports that Kazakh mathematician Mukhtarbay Otelbayev may have solved an ...

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 numerical solution of flow problems usually requires bounded domains although the physical problem may take place in an unbounded or substantially larger domain. In this case, artificial ...

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 ...

Erica Grace Cabanilla, my ERDT administrator, who took charge of all my stipends, reminded me gently that I am supposed to give my exit report on Jan. 26 as Visiting Researcher, although my ...

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 ...

We consider the incompressible Navier-Stokes equation with a fractional power α ∈ [1, ∞) of the Laplacian in the three-dimensional case. We prove the existence of a smooth solution with arbitrarily ...