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 ...

The study of free boundary problems in the Navier-Stokes equations addresses the subtle interplay between the dynamics of viscous, incompressible fluids and the evolution of interfaces whose locations ...

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 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 ...

Turbulence is one of the least understood phenomena of the physical world. Long considered too hard to understand and predict mathematically, turbulence is the reason the Navier-Stokes equations, ...

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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 ...

MATHEMATICS is a universal language. Even so, a Kazakh mathematician’s claim to have solved a problem worth a million dollars is proving hard to evaluate – in part because it is written in Russian.