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 Navier-Stokes equations describe how water flows in turbulent situations. williams_jt / Flickr A huge mathematical breakthrough might have just been made, but a language barrier is slowing ...

Martin Hairer, Jonathan C. Mattingly, Ergodicity of the 2D Navier-Stokes Equations with Degenerate Stochastic Forcing, Annals of Mathematics, Second Series, Vol. 164 ...

The Navier-Stokes equation (NSE) rules all of fluid dynamics, including, it was supposed to be, turbulence. Fluid dynamics, aerodynamics and turbulence were supposed to be together always.

In this article we consider a two-level finite element Galerkin method using mixed finite elements for the two-dimensional nonstationary incompressible Navier-Stokes equations. The method yields a ...

Yet, despite all this progress, one of the biggest unsolved mysteries in physics and mathematics remains—the Navier-Stokes equation.

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.

Gifted centers on the Navier-Stokes problem, prompting many viewers of the 2017 drama to wonder what the unsolved math problem is â and whether real-life mathematicians have since solved it ...

Two mathematicians prove that under certain extreme conditions, the Navier-Stokes equations output nonsense.