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 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 ...

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, ...

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 ...

Several University of Texas at Austin mathematics faculty, including an incoming assistant professor, have seen their work spotlighted in the science publication Quanta in recent weeks. Distinct in 3D ...

Turbulence, the splintering of smooth streams of fluid into chaotic vortices, doesn’t just make for bumpy plane rides. It also throws a wrench into the very mathematics used to describe atmospheres, ...

This is a preview. Log in through your library . Abstract Some partial differential equations encountered in physical applications are of incompletely parabolic type; the Navier-Stokes equations in ...

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.

What if engineers could design a better jet with mathematical equations that drastically reduce the need for experimental testing? Or what if weather prediction models could predict details in the ...